Question

The point (-1, 3) is the turning point of the graph with equation y = x2 + ax + b,

where a and b are integers.
Find the values of a and b.

Answer 1

a = 2

b = 4

Explanation:

Δy = 2x + a.................for turning point, Δy/Δx = 0.

Δx

0 = 2x + a

x = -a/2.........from ( -1, 3), x = -1...............so,

-1 = -a/2.................a = 2.

y = x^2 + ax + b.

y = 3 , a = 2.................substitute.

3 = (-1)^2 + 2(-1) + b

3 = 1 -2 + b

b = 4

Answer 2

The turning point of a parabola is the vertex

Vertex form of a quadratic equation:
`\sf y=a(x-h)^2+k`

(where (h, k) is the vertex and a is the coefficient of the variable x²)

Given:

• 
  `\sf y=x^2+ax+b`
• vertex = (-1, 3)

Therefore, a = 1

Substituting a = 1 and the given vertex into the equation:

`\sf \implies y=1(x-(-1))^2+3`

`\sf \implies y=(x+1)^2+3`

`\sf \implies y=x^2+2x+1+3`

`\sf \implies y=x^2+2x+4`

Therefore, a = 2 and b = 4