How do you write a quadratic equation with vertex (-2,-3) and goes through the point (-4,25)?

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Answer 1 · 2018-07-02T05:58:40

$y = 7(x + 2)^2 - 3 " or "y = 7x^2 + 28x + 25$

Given: quadratic equation with vertex $(-2, -3)$ , through $(-4, 25)$

Vertex form: $y = a(x-h)^2 + k$ , where vertex $(h, k)$ and $a$ is a constant.

$y = a(x + 2)^2 - 3$

Solve for $a$ using the point $(-4, 25)$ :

$25 = a(-4 + 2)^2 - 3$

$25 = (-2)^2a - 3$

$25 = 4a - 3$

$28 = 4a$

$a = 28/4 = 7$

Equation: $y = 7(x + 2)^2 - 3$

To put it in general form:

$y = 7(x^2 + 4x + 4) - 3$

$y = 7x^2 + 28x + 25$

graph{7(x + 2)^2 - 3 [-5, 5, -5, 25]} #