Answer:
(1.06, 0), (-3.06, 0)
Step-by-step 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) = [tex]\pm\sqrt{17}[/tex]
Divide both sides by 2.
x + 1 = [tex]-1\pm\frac{\sqrt{17}}{2}[/tex]
Subtract 1 from both sides.
x = [tex]\left \{ {{-1+\frac{\sqrt{17}}{2} ~= ~1.06} \atop {-1-\frac{\sqrt{17}}{2}~=~-3.06}} \right.[/tex]
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)
