Question

Find the x-intercepts of the parabola with

Answer 1

Answer:

$x_1=3.55$

$x_2=-1.55$

Step-by-step explanation:

we know that

If the vertex is  (1,-13) and the y-intercept is  (0.-11) (y-intercept above the vertex), we have a vertical parabola open upward

The equation of a vertical parabola written in vertex form is equal to

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

where

a is a coefficient

(h,k) is the vertex

substitute the given value of the vertex

$y=a(x-1)^2-13$

Find the value of a

Remember that we have the y-intercept

For x=0, y=-11

substitute

$-11=a(0-1)^2-13$

$a=13-11\\a=2$

so

$y=2(x-1)^2-13$

Find the x-intercepts

For y=0

$2(x-1)^2-13=0$

$2(x-1)^2=13$

$(x-1)^2=6.5$

$x-1=\pm\sqrt{6.5}$

$x=1\pm\sqrt{6.5}$

$x_1=1+\sqrt{6.5}=3.55$

$x_2=1-\sqrt{6.5}=-1.55$