Mathematics: 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.

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Find the x-intercepts of the parabola with vertex

Ответ:

elizabethhubbe

10.03.2022

Mathematics

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

Step-by-step 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

$0=3(x+3)^{2}-14$

$3(x+3)^{2}=14$

$(x+3)^{2}=14/3$

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

therefore

the x-intercepts are

$(-3-\sqrt{\frac{14}{3}},0)$ and $(-3+\sqrt{\frac{14}{3}},0)$

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

see the attached figure to better understand the problem

Find the x-intercepts of the parabola with vertex (-3,-14) and y-intercept (0,13). write your answer

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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.

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