Question

HELP PLEASE find the x-intercepts of the parabola with vertex -1,-17 and y-intercept 0,-13. Write your answer in this form: (x1,y1), (x2,x2). if necessary, round to the nearest hundredth.

Answer 1

(1.06, 0), (-3.06, 0)

Explanation:

Substitute the vertex (-1, -17) and the point (0, -13) into the vertex form of a parabola: y = a(x - h)^2 + k. Solve for a.

-13 = a(0 - (-1))^2 - 17

Simplify this equation.

-13 = a(1)^2 - 17

Evaluate the exponent.

-13 = a - 17

Add 17 to both sides.

4 = a

Now substitute the vertex and the a-value into the vertex form of a parabola: y = a(x - h)^2 + k.

y = 4(x - (-1))^2 - 17

Simplify.

y = 4(x + 1)^2 - 17

Now to find the x-intercepts, make y = 0.

4(x + 1)^2 - 17 = 0

Add 17 to both sides.

4(x + 1)^2 = 17

Square root both sides.

2(x + 1) =
`\pm√(17)`

Divide both sides by 2.

x + 1 =
`-1\pm(√(17))/(2)`

Subtract 1 from both sides.

x =
`\left \{ {{-1+(√(17))/(2) ~= ~1.06} \atop {-1-(√(17))/(2)~=~-3.06}} \right.`

Since you want the answers in the form (x1, y1), (x2, y2) and for the answers to be rounded to the nearest hundredth, your final answers are:

(1.06, 0), (-3.06, 0)