Question

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

y = –0.25(x – 4)^2 2 – 2


vertex, (2, –4); y-intercept, –6


vertex, (–4, 0); y-intercept, –6


vertex, (4, –2); y-intercept, –6


vertex, (–2, 4); y-intercept, –6

Answer 1

vertex, (4, –2); y-intercept, –6.

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
`((-b)/(2a),y((-b)/(2a)) )` where a=-0.25 and b=2. So,

`(-b)/(2a)= (-2)/(-0.5)=4`

`y((-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.

Answer 2

vertex, (4, –2); y-intercept, –6

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.