Answer:
a = 2
b = 4
Step-by-step 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:
The turning point of a parabola is the vertex
Vertex form of a quadratic equation: [tex]\sf y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex and a is the coefficient of the variable x²)
Given:
Therefore, a = 1
Substituting a = 1 and the given vertex into the equation:
[tex]\sf \implies y=1(x-(-1))^2+3[/tex]
[tex]\sf \implies y=(x+1)^2+3[/tex]
[tex]\sf \implies y=x^2+2x+1+3[/tex]
[tex]\sf \implies y=x^2+2x+4[/tex]
Therefore, a = 2 and b = 4
