Question

Help: I am stuck on this maths question on quadratics and turning points (image attached).

I have got 2 marks out of 4 but I am unsure how to get the last two marks because I have already got my answer (-2.5) but it does not give me anything.

Here is what I have written:
y intercept = (0,-14)
roots = (2,0), P
0=2^2+2b-14
0=4+2b-14
0=2b-10
2b=10
b=5
y=x^2+5x-14=0

then we have to complete the square
half 5 = 2.5
(x+2.5)^2 = (x+2.5)(x+2.5) = x^2-5x-6.25
find the difference:
-14-(2.5)^2=-20.25
flip the signs
turning point = (-5/2,-81/4)
The x-coordinate of the turning point is -20.25

Answer 1

the x- coordinate of the turning point = - 2.5

Explanation:

given

x² + bx + c

c is the value of the y- coordinate where the curve crosses the y- axis, so c= - 14

x² + bx - 14

given x = 2 is a root , then equating to zero gives

2² + 2x - 14 = 0

4 + 2x - 14 = 0

- 10 + 2x = 0 ( add 10 to both sides )

2x = 10 ( divide both sides by 2 )

x = 5

then equation is

x² + 5x - 14 = 0 ← in standard form

(x + 7)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 2 = 0 ⇒ x = 2

the roots are x = - 7, x = 2

the x- coordinate of the vertex is at the midpoint of the roots , that is

x- coordinate of the turning point = (- 7 + 2) ÷ 2 = - 5 ÷ 2 = - 2.5