Vertex Form

​Which quadratic function in vertex form can be represented by the graph that has a vertex (3, -7) and passes through the point (1, -10)?

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Vertex form is y = a(x - h)² + k
(h,k) are the coordinates of the vertex

Substitute the vertex, (3,-7) in for h and k, and substitute the point (1, -10) in for x and y into vertex form, to get a.

y = a(x - h)² + k {vertex form}
-10 = a(1 - 3)² - 7 {substituted the vertex and point into vertex form}
-10 = a(-2)² - 7 {worked inside parentheses}
-10 = 4a - 7 {squared the -2}
-3 = 4a {added 7 to each side}
a = -3/4 {divided each side by 4}

In vertex form, substitute -3/4 for a, 3 for h, and -7 for k.

​y = (-3/4)(x - 3)² - 7

Ask the House

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