Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 3, - 14), thus
y = a(x + 3)² - 14
To find a substitute (0, - 13) into the equation
- 13 = 9a - 14 ( add 14 to both sides )
9a = 1 ( divide both sides by 9 )
a = [tex]\frac{1}{9}[/tex], hence
y = [tex]\frac{1}{9}[/tex](x + 3)² - 14 ← equation of parabola
To find the x- intercepts let y = 0
[tex]\frac{1}{9}[/tex](x + 3)² - 14 = 0
Multiply through by 9
(x + 3)² - 126 = 0 ( add 126 to both sides )
(x + 3)² = 126 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{126}[/tex] = ± 3[tex]\sqrt{14}[/tex]
Subtract 3 from both sides
x = - 3 ± 3[tex]\sqrt{14}[/tex]
The x- intercepts are therefore
x = - 3 - 3[tex]\sqrt{14}[/tex] ≈ - 14.22 ( to 2 dec. places ) or
x = - 3 + 3[tex]\sqrt{14}[/tex] ≈ 8.22 ( to 2 dec. places )
