Question

Which of the following is the graph of the quadratic function y - x? +10x+16 ?
A. Graph C
B. Graph B
C. Graph A
D. Graph D

Answer 1

Find the vertex:

$\textrm{Use the formula } \frac{-b}{2a} \textrm{ to find the vertex}\\ \\ \frac{-10}{2} = -5\\ \\ \textrm{In order to find the y value plug in -5 back into the function}\\ \\ y=(-5)^2+10(-5)+16\\ y=-9\\\\ \textrm{The vertex of the function is} (-5,-9)$

Determine if the parabola will open up or down:

$a > 0 \\ \\ 1>0$

Since the value of a is positive, the parabola will open upwards

Find the x and y intercepts:

Factor $y = x^2+10x + 16$ to find the x intercepts

(x+8)(x+2)

x + 8 = 0

x = -8

x + 2 = 0

x = -2

x intercepts:

x = -2

x = -8

Find the y intercept

$y = 0^2+10(0) + 16\\\\ y=16$

Hence, C. Graph A best represents the quadratic function $y = x^2+10x + 16$