Answer:
Below in bold.
Step-by-step explanation:
f(x) = 1/2x^2 + 4x
Convert to vertex form:
f(x) = 1/2(x^2 + 8x)
= 1/2 [(x + 4)^2 - 16]
= 1/2(x + 4)^2 - 8 <------ Vertex form.
So the Vertex is at (-4, - 8).
Axis of symmetry is x = -4.
y -intercept (when x = 0) = 8-8 = 0.
Answer:
see explanation
Step-by-step explanation:
given a quadratic function in standard form
f(x) = ax² + bx + c ( a ≠ 0 ) , then
the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = [tex]\frac{1}{2}[/tex] x² + 4x ← is in standard form
with a = [tex]\frac{1}{2}[/tex] , b = 4 , c = 0 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{4}{1}[/tex] = - 4
substitute x = - 4 into f(x) for corresponding y- coordinate of vertex
f(- 4) = [tex]\frac{1}{2}[/tex] (- 4)² + 4(- 4) = [tex]\frac{1}{2}[/tex] × 16 - 16 = 8 - 16 = - 8
vertex = (- 4, - 8 )
the equation of the axis of symmetry is a vertical line passing through the vertex with equation
x = c ( c is the x- coordinate of the vertex ) , then equation of axis of symmetry is
x = - 4
to find the y- intercept substitute x = 0 into f(x)
f(0) = [tex]\frac{1}{2}[/tex] (0)² + 4(0) = 0 + 0 = 0
then y- intercept is 0