Question

Find the x-intercepts of the parabola with

vertex (-3,-14) and y-intercept (0,13).
Write your answer in this form: (X1,Y1), (X2,42).
If necessary, round to the nearest hundredth.

Answer 1

`(-5.16,0)` and
`(-0.84,0)`

Explanation:

step 1

Find the equation of the quadratic equation

we know that

The equation of a vertical parabola into vertex form is equal to

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

where

(h,k) is the vertex

a is a coefficient

we have that

(h,k)=(-3,-14)

substitute

`y=a(x+3)^(2)-14`

Remember that the y-intercept is the point (0,13)

substitute the value of x and y in the equation and fond the value of a

For x=0, y=13

`13=a(0+3)^(2)-14`

`13=9a-14`

`9a=27`

`a=3`

The equation is

`y=3(x+3)^(2)-14`

step 2

Find the x-intercepts

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

so

`0=3(x+3)^(2)-14`

`3(x+3)^(2)=14`

`(x+3)^(2)=14/3`

`x+3=(+/-)\sqrt{(14)/(3)}\\ \\x=-3(+/-)\sqrt{(14)/(3)}`

therefore

the x-intercepts are

`(-3-\sqrt{(14)/(3)},0)` and
`(-3+\sqrt{(14)/(3)},0)`

or

`(-5.16,0)` and
`(-0.84,0)`

see the attached figure to better understand the problem