Question

What is the vertex and equation for axis of symmetry of f(x)= x^2 +4x+3

Answer 1

see explanation

Explanation:

Given a quadratic function in standard form ax² + bx + c : a ≠ 0

Then the axis of symmetry and the x- coordinate of the vertex, since the vertex lies on the axis of symmetry is

x = -
`(b)/(2a)`

f(x) = x² + 4x + 3 ← is in standard form

with a = 1, b = 4, hence

x = -
`(4)/(2)` = - 2

Equation of axis of symmetry is x = - 2

Substitute x = - 2 into f(x) for corresponding y- coordinate of vertex

f(- 2) = (- 2)² + 4(- 2) + 3 = 4 - 8 + 3 = - 1

Hence vertex = (- 2, - 1)

Answer 2

Vertex: (- 2, -1)

axis of symmetry: x= - 2

Explanation:

f(x)=x^2+4x+3

f(x)=(x^2+4x+4)+3-4.......complete the square

f(x)=(x+2)^2-1...................write in vertex form