Question

Identify the vertex and the y-intercept of the graph of the function.

Answer 1

Answer:

vertex, (4, –2); y-intercept, –6

Step-by-step explanation:

The equation is written in vertex form $y = a(x-h)^2 + k$ where the vertex is (h,k).

The vertex here is (4, -2). This means the solution is vertex, (4, –2); y-intercept, –6.

Answer 2

Answer:

vertex, (4, –2); y-intercept, –6.

Step-by-step explanation:

$y=-0.25(x-4)^{2}-2$

$y=-0.25(x^{2}-8x+16)-2$

$y=-0.25x^{2}+2x-4-2$

$y=-0.25x^{2}+2x-6$

the vertex is $(\frac{-b}{2a},y(\frac{-b}{2a}) )$ where a=-0.25 and b=2. So,

$\frac{-b}{2a}= \frac{-2}{-0.5}=4$

$y(\frac{-b}{2a})=-0.25(4)^{2}+2(4)-6= -4+8-6=-2$

Then, the vertex is (4,-2) and the intercept is y(0)= -0.25(0)+2(0)-6 = -6. So, the answer is the third option.