Write the equation in vertex form and identify the vertex

Consider g(x) = −x² + 12x − 32. Write the equation in vertex form and identify the vertex.

---

g(x) = -x² + 12x - 32 is in standard form.
a = -1, b = 12, and c = -32

Find the x-coordinate of the vertex.
x = -b/2a
= -12/2(-1) {substituted 12 for b and -1 for a}
x = 6 {simplified}

Find the y-coordinate of the vertex by substituting 6 in for x.
y = -(6)² + 12(6) - 32 {substituted 6 for x into original equation to find y}
= -36 + 72 - 32 {evaluated exponent and multiplied}
y = 4 {added and subtracted}

The coordinates of the vertex are (6,4).

Vertex form of a quadratic function is g(x) = a(x - h)² + k
(h,k) are the (x,y) coordinates of the vertex
a is the same in vertex form as it is in standard form

​Substitute into vertex form.
g(x) = -(x - 6)² + 4 is vertex form {substituted -1 for a, 6 for h, and 4 for k, into vertex form}
Again, the vertex is (6,4)

Ask the House