Question

Write y=x^2+16x−7​ in vertex form. Then identify the vertex.

The vertex form of the function is y=_____

The vertex is (__,__)

Answer 1

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

Step-by-step explanation:

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

• (h , k) are the coordinates of the vertex point
• a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
• $h=\frac{-b}{2a}$
• k is the value of y when x = h

∵ y = x² + 16x - 7

∵ y = ax² + bx + c

∴ a = 1 , b = 16 , c  = -7

∵ $h=\frac{-b}{2a}$

∴ $h=\frac{-16}{2(1)}$

∴ h = -8

To find k substitute y by k and x by -8 in the equation above

∵ k is the value of y when x = h

∵ h = -8

∴ k = (-8)² + 16(-8) - 7 = -71

∵ The vertex form of the quadratic equation is y = a(x - h)² + k

∵ a = 1 , h = -8 , k = -71

∴ y = (1)(x - (-8))² + (-71)

∴ y = (x + 8)² - 71

∵ (h , k) are the coordinates of the vertex point

∵ h = -8 and k = -71

∴ The vertex is (-8 , -71)

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

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