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