Question

for all functions of the form \\(f(x) = ax^2 + bx + c\\), which is true when \\(b = 0\\)?

• the graph will always have zero x-intercepts.
• the function will always have a minimum.
• the y-intercept will always be the vertex.
• the axis of symmetry will always be positive.

Explanation:

Analyze the quadratic function when b = 0

Using the Quadratic Vertex and Axis of Symmetry knowledge points

$$
LATEXBLOCK0
$$

Evaluate the y-intercept of the function

Using the Quadratic Vertex knowledge point

$$
LATEXBLOCK1
$$

Evaluate the remaining options

Using the Axis of Symmetry and x-intercept of a Quadratic Function knowledge points

$$
LATEXBLOCK2
$$

Answer:

• The graph will always have zero x-intercepts.
• The function will always have a minimum.
• The y-intercept will always be the vertex. (Correct answer)
• The axis of symmetry will always be positive.