Tamara J. answered • 12/06/12

Math Tutoring - Algebra and Calculus (all levels)

The vertex form of a quadratic function looks like the following:

**y = a(x - h)**^{2}** + k** , where **(h, k)** is the vertex of the graph of the function.^{}

Given the graph of a quadratic function whose vertex is at (-5, 7), where -5 = h and 7 = k, we can write an equation for the quadratic function in vertex form:

y = a(x - h)^{2} + k , (h, k) = (-5, 7)

y = a(x - (-5))^{2} + 7

y = a(x + 5)^{2} + 7 ==> where a = 1

**y = (x + 5)**^{2}** + 7**

Now we can convert this into the standard form of a quadratic equation, which looks like the following:

**y = ax**^{2}** + bx + c**

y = (x + 5)^{2} + 7

y = (x + 5)(x + 5) + 7

y = (x^{2} + 5x + 5x + 25) + 7

**y = x**^{2}** + 10x + 32** ==> where a = 1, b = 10, c = 32

Bart M.

08/10/16