Answer:
x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given the graph intersects the y- axis at (0, - 18), then substitute the coordinates into the equation y = x² + bx + c
- 18 = 0 + 0 + c ⇒ c = - 18
In the same way substitute (6, 0) into the equation
0 = 6² + 6b - 18
0 = 36 + 6b - 18
0 = 18 + 6b ( subtract 18 from both sides )
- 18 = 6b ( divide both sides by 6 )
- 3 = b
Hence equation is
y = x² - 3x - 18
Given the equation in standard form : y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - 3x - 18 is in standard form
with a = 1, b = - 3, c = - 18, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{-3}{2}[/tex] = [tex]\frac{3}{2}[/tex]
The x- coordinate of the turning point is [tex]\frac{3}{2}[/tex]
