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levacccp [35]
3 years ago
11

HELP ME!! im so stumped. will give brainliest!

Mathematics
1 answer:
Olegator [25]3 years ago
4 0

Answer:

x=1+\sqrt{3} and x=1-\sqrt{3}

Step-by-step explanation:

We have been given the parabola with vertex (1, -9) and y intercept at (0, -6).

Now we need to find the x-intercepts of that parabola. So first we begin by finding the equation of parabola using vertex formula:

y=a\left(x-h\right)^2+k

Vertex for this formula is given by (h,k)

Compare that with given vertex (1,-9), we get: h=1, k=-9

So plug these into vertex formula:

y=a\left(x-1\right)^2-9...(i)

Plug given point (0, -6). into (i)

-6=a\left(0-1\right)^2-9

-6=a\left(-1\right)^2-9

-6=a\left(1\right)-9

-6+9=a

3=a

Plug a=3 into (i)

y=3\left(x-1\right)^2-9

Now to find x-intercept, we just plug y=0 and solve for x

y=3\left(x-1\right)^2-9

0=3\left(x-1\right)^2-9

9=3\left(x-1\right)^2

3=\left(x-1\right)^2

\pm \sqrt{3}=x-1

1+\pm \sqrt{3}=x

Hence final answer are

x=1+\sqrt{3} and x=1-\sqrt{3}

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