Answer:
the x- coordinate of the turning point is - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Given
y = x² + bx + c with y- intercept = (0, - 14 ) then c = - 14 , so
y = x² + bx - 14
To find b substitute (2, 0 ) into the equation
0 = 2² + 2b - 14
0 = 4 + 2b - 14
0 = - 10 + 2b ( add 10 to both sides )
10 = 2b ( divide both sides by 2 )
5 = b , then
y = x² + 5x - 14
Given a parabola in standard form y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the turning point is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 5x - 14 ← is in standard form
with a = 1 and b = 5 , then
x- coordinate of turning point = - [tex]\frac{5}{2}[/tex]
