Question

Find the x-intercepts of the parabola with vertex (5,-4) and y-intercept (0,96). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth. ​

Answer 1

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

Explanation:

we know that

The equation of the given parabola is

`(y-k)=a(x-h)^(2)`

we have

the vertex is the point (5,-4)

substitute

`(y+4)=a(x-5)^(2)`

The y-intercept is the point (0,96)

substitute and solve for a

`(96+4)=a(0-5)^(2)`

`100=a(25)`

`a=100/25=4`

The equation of the vertical parabola is equal to

`(y+4)=4(x-5)^(2)`

Find the x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero

For y=0

`4=4(x-5)^(2)`

Simplify

`1=(x-5)^(2)`

Rewrite

`(x-5)^(2)=1`

square root both sides

`(x-5)=(+/-)1`

`x=(+/-)1+5`

`x=(+)1+5=6`

`x=(-)1+5=4`

therefore

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)