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Write the equation in vertex form for a quadratic whose vertex is (-4, 6) and contains the point (-5, 4).

a. y = (x + 4)^2 + 6
b. y = (x - 4)^2 + 6
c. y = (x + 4)^2 - 6
d. y = (x - 4)^2 - 6

1 Answer

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Final answer:

To find the quadratic equation in vertex form with a given vertex and a point, we use the vertex form equation (y = a(x - h)^2 + k) and substitute the vertex and point values to solve for 'a'. The correct equation, based on the provided vertex (-4, 6) and point (-5, 4), is y = -2(x + 4)^2 + 6, which is not listed among the provided options.

Step-by-step explanation:

The question asks to write the equation of a quadratic in vertex form, where the vertex is given as (-4, 6), and the quadratic passes through the point (-5, 4). A quadratic equation in vertex form is written as y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Given the vertex (-4, 6), we substitute h = -4 and k = 6 into the vertex form, which yields y = a(x + 4)^2 + 6.

To find the value of 'a', we use the point (-5, 4) which lies on the parabola. We substitute x = -5 and y = 4 into the equation:

4 = a(-5 + 4)^2 + 6

4 = a(1)^2 + 6

4 = a + 6

Now we solve for 'a':

a = 4 - 6

a = -2

Then we substitute 'a' into the vertex form of the equation:

y = -2(x + 4)^2 + 6

Therefore, none of the given options (a, b, c, or d) is correct. The correct equation in vertex form is y = -2(x + 4)^2 + 6.

User Rick Weller
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