which is the graph of a quadratic equation that has a negative discriminant
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The equation of which graph has a negative discriminant? The equation of which graph has a negative discriminant? A. The graph shows a parabola opening up with a vertex at 2 comma negative 1. B. The graph shows a parabola opening up with a vertex at negative 1 comma negative 3. C. The graph shows a parabola opening down with a vertex at negative 1 comma negative 1. D. The graph shows a parabola opening down with a vertex at negative 1 comma 0. 2/21/2015 | May from Meredith, NH | 1 Answer | 0 Votes.
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Quadratic Functions The quadratic function f(x) = a(x-h) 2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).
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- Note: There is a method called completingthesquarethat will transform a quadratic function written in standard form into vertex form. This method will not be taught in this course since it is easier to ﬁnd the vertex with the x= −b 2a computation. The x-intercepts of the quadratic function can be found by setting the quadratic equation equal to zero and solving for x. This can be done in a variety of ways. If the quadratic function is in the standard form, then you can use the quadratic formula: x= −b± √ b2 −4ac 2a, provided b2 −4ac≥ 0
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- The coefficient of the unsquared part is 20, and this is also the value of 4p, so p = 5. Since the x part is squared and p is negative, then this is a regular parabola that opens downward. This means that the directrix, being on the outside of the parabola, is five units above the vertex.
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Quadratic Equations Review Matching Cards Quadratic Equations Review Matching Cards. Key Words: Quadratics, Roots, Completing the Square, Discriminant, Quadratic Graphs. This is a group-work matching activity covering everything to do with Quadratics. It takes about 2 lessons to do fully. Students need to match the equation to its roots, completed square form, discriminant, curve and find the coordinates of the minimum. Designed for and tested on top set Year 10 groups but would work equally well with year 12s for Core 1.
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Solving Quadratic Equations A quadratic equation with real numbers as coefficients can have the following: 1  Two different real roots if the discriminant b 2 – 4 ac is a positive number. 2  One real root if the discriminant b 2 – 4 ac is equal to 0. 3  No real root if the discriminant b 2 – 4 ac is a negative number.
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Quadratic Functions in Standard Form D-y intercepts of the graph of a quadratic function. . 1  has a. 2  intercept at. . . 3  has a. 4  intercept at. . . 5  has a. 6  intercept at. . 7  Use the applet window to check the. 8  intercept for the quadratic functions in the above example. 9  Use the applet window to check the. 10  intercept is at the point. 11  for different values of. .
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Algebra Examples The discriminant of a quadratic is the expression inside the radical of the quadratic formula. Substitute in the values of , , and . Evaluate the result to find the discriminant.
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- First, I have to find the x-intercepts of the associated quadratic, because the intercepts are where y = x2 3x + 2 is equal to zero. Graphically, an inequality like this is asking me to find where the graph is above or below the x-axis. It is simplest to find where it actually crosses the x-axis, so I'll start there.
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Quadratic equation If the discriminant is zero, there is only one solution. If the discriminant is positive, then the ± symbol means you get two answers. The solutions of this equation correspond to the x-intercepts of the parabola. y = ax 2 + bx + c.So, you can also use the discriminant to find the number of x-intercepts of a parabola.Parabola with two x-intercepts. (positive discriminant). Parabola with one x-intercept. (zero discriminant). Parabola with no x-intercept. (negative discriminant). Example 1: Solve the quadratic equation.f the discriminant is zero, there is only one solution. If the discriminant is positive, then the ± symbol means you get two answers. The solutions of this equation correspond to the x-intercepts of the parabola. y = ax 2 + bx + c.
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- Just as changing a from positive to negative reflected the graph across the x-axis, we can hypothesize that the same will hold true when b is negative. Let's take a look at the graph y = a sin (bx + c) where b = -1/2, -1, and -2, a = 1, and c = 0.
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- Definition of Discriminant. The Discriminant of an equation gives an idea of the number of roots and the nature of roots of the equation. If ax2 + bx + c = 0 is a quadratic equation, then the Discriminant of the equation, i.e. D = b2 - 4ac. If discriminant (D) is equal to 0 then the equation has one real solution.
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- Find the equation of the quadratic function whose graph has vertex (3;5) andy-intercept 4.(a) f(x) = (x 3) 2 +5 (d) f(x) = (x+3) 2 +5(b) f(x) = (x 3) 2 13 (e) None of these(c) f(x) = (x+3) 2 +54.3 #61. Find the minimum value of the function f(x) = 2x 2 +12x 3.(a) 57 (d) 51(b) 29 (e) None of these(c) 214.3 #62. Find the minimum value of the quadratic function f(x) = 4x 2 8x+3.(a) 5 (d) 15(b) 1 (e) 35(c) 34.3 #81.
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Can we stop using 'mouth breather' as an insult September 11, 2010 3:51 AM Subscribe #c=10#. The solution to any of these problems is known as the quadratic equation: #x = (-b +- sqrt(b^2 - 4 a c))/(2a)#. The reason there is a #+# and a #-# in the top just means that there are two possible answers for x, and you need to try both signs to get both answers. The discriminant is just defined as the stuff in the square root of the expression:
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Quadratic Functions Standard form provides clues to what the graph of a quadratic function will look like. By inspecting a quadratic equation in standard form, y (x) = ax 2 + bx + c, you can get an idea of what the graph will look like. The leading coefficient tells you the direction the parabola opens, specifically. if a. if a. In addition, the constant c is the y-intercept of the quadratic function. This fact can be derived mathematically by setting x = 0 (remember, points lying on the y-axis must have x-coordinate equal to zero) in the standard form of a quadratic equation yielding, y (0) = a · 0 2 + b · 0 + c.
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-     3 2 Here we put the x term first. y x.     (3) 2 Here we factored out a -1. Now we are ready to graph. Since we already factored out the negative. There is a negative inside the function, so we need to use rule 6 of the. EXAMPLE: Sketch. 3. y x.    1 2 by using transformations. Be careful you don’t confuse this with the square root graphs we just did. This one looks different.
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- In the vertex form of the quadratic, the fact that (h, k) is the vertex makes sense if you think about it for a minute, and it's because the quantity x – h is squared, so its value is always zero or greater; being squared, it can never be negative.
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- Tap for more steps... The maximum or minimum of a quadratic function occurs at x=−b2ax=-b2a. If aa is negative, the maximum value of the function is f(−b2a)f-b2a. If aa is positive, the minimum value of the function is f(−b2a)f-b2a. fminfmin(x)=ax2+bx+cx=ax2+bx+c occurs at x=−b2ax=-b2a. Find the value of xx equal to −b2a-b2a.
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The graph of a radical function If we compare this to the square root function. We will notice that the graph stretches or shrinks vertically when we vary a. In the graph below we have radical functions with different values of a. Is the reflection in the x-axis of the graph. Another square root equation would be. If you look at the graphs above which all have c = 0 you can see that they all have a range ≥ 0 (all of the graphs start at x=0 since there are no real solutions to the square root of a negative number).
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Quadratic Functions (General Form) Quadratic functions and the properties of their graphs such as vertex and x and y intercepts are explored interactively using an html5 applet. A-Definition of a quadratic function A quadratic function f is a function of the form f(x) = ax + bx + c where.
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- 1 It is a quadratic trinomial with coefficients a = 1, b = 6, and c = −5. 2  Its discriminant is D = b 2 − 4 · a · c = 6 2 − 4 · 1 · (−5) = 56, which is not a perfect square so we must factor the expression using the completing the square method. 3  The next four steps convert the expression to completed square form. If D is negative then the above formula contains the square root of a negative number. 2  Over the real numbers this is not allowed and means that the quadratic trinomial can't be factored, but over the complex numbers this is no problem. 3  This case is described in detail below. 4  Identify the form of the expression.
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- The discriminant refers to a particular section of the quadratic formula, which is #-b +- sqrt(b^2 - 4ac)/(2a)#. The discriminant is only the following part of the formula, the part under the radical/square root sign: #sqrt(b^2 - 4ac)#. In this case, the discriminant would be: #(-4)^2 - 4(1)(10)#. Or just #16 - 40# which is equal to #-24#.
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- Quadratic discriminant analysis is an adaptation of linear discriminant analysis to handle data where. the variance-covariance matrices of the di erent classes are markedly di erent. For g = 2 the logistic. regression model, tted using R’s glm() function, is closely analagous to the linear discriminant model.
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- If the discriminant is a positive number, then we get two real. numbers as answers to the equation. One of the answers comes from following the + path on the. The other comes from following the − path.
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She Loves Math Now remember that we said that when a quadratic crosses the x axis (when y = 0), we call that point an x-intercept, root, zero, solution, value, or just “ solving the quadratic ”. And also remember that not all of the “solutions” were real – when the quadratic graph never touched the x axis.
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Graphing Quadratic Functions The vertex is an important coordinate to find because we know that the graph of the parabola is symmetric with respect to the vertical line passing through the vertex. The coordinate of the vertex of a quadratic equation in standard form (y = ax2 + bx + c) is (-b/2a, f(-b/2a)), where x = -b/2a and y = f(-b/2a).