Find the vertex, zero(s), and y-intercept of the graph of y = –x2 + 4x + 32. a. vertex: (2,36); zeros: (–4,0), (8,0) y-intercept: (0,32) b. vertex: (36,2); zeros: (–4,0), (8,0) y-intercept: (32,0) c. vertex: (2,3); zeros: (–4,0), (8,0) y-intercept: (0,16) d. vertex: (2,36); zeros: (–8,0), (4,0) y-intercept: (0,32)

The correct option is A.

Step-by-step explanation:

The given equation is

Put x=0, in the given equation.

The y-intercept is (0,32).

Put y=0, to find the x-intercept.

Therefore the y-intercepts are (-4,0) and (8,0).

The vertex of a parabola is

Put x=2 in the given function.

The vertex is (2,36).

Therefore option A is correct.

Option (a) is correct.

Vertex: (2,36); zeros: (–4,0), (8,0) y-intercept: (0,32)

Step-by-step explanation:

Consider the given equation

We have to find vertex, zero(s), and y-intercept.

First we find the vertex, For The general form of a quadratic is

the coordinate of the vertex (h, k)  is given as and

Here, a= -1 , b= 4 and  c = 32

and,

Thus vertex of  is ( 2, 36)

Now, we find the zeros,

Put y = 0, we get,

This is a quadratic equation of the form

Hence, we can find zero using middle term splitting method,

4x can be written as 8x - 4x

Thus,

or

or

Thus, zeros are (-4,0) and (8,0) .

Now to calculate y intercept put x = 0 in

We get , y= 32.

The same can be seen through graph as below.

Thus, option (a) is correct.

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