Question

Find the vertex, zero(s), and y-intercept of the graph of y = 2x2 + 8x – 90. A. Vertex: (–2,–98); zeros: (–5,0), (9,0) y-intercept: (0,–90) B. Vertex: (2,–98); zeros: (–5,0), (9,0) y-intercept: (0,90) C. Vertex: (2,98); zeros: (5,0), (–9,0) y-intercept: (0,–90) D. Vertex: (–2,–98); zeros: (5,0), (–9,0) y-intercept: (0,–90)

Answer 1

vertex is (-2,-98)

zeros are (5,0) (-9,0)

y-intercept is (0,-90)

Explanation:

we are given

`y=2x^2+8x-90`

Vertex:

we can use vertex formula

`y=ax^2+bx+c`

`x=-(b)/(2a)`

we can compare and find a,b and c

a=2 , b=8 and c=-90

so, we can plug it in formula

`x=-(8)/(2* 2)`

`x=-2`

now, we can find y-value

`y=2(-2)^2+8(-2)-90`

`y=-98`

so, vertex is (-2,-98)

zeros:

we can set y=0

and then we can solve for x

`y=2x^2+8x-90=0`

we can factor it

`2(x-5)(x+9)=0`

`x=5,x=-9`

zeros are

(5,0) (-9,0)

y-intercept:

we can plug x=0 and find y

`y=2(0)^2+8(0)-90`

`y=-90`

So, y-intercept is (0,-90)