For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?
a. the graph will always have zero x-intercepts.
b. the function will always have a minimum.
c. the y-intercept will always be the vertex.
d. the axis of symmetry will always be positive.

The correct answer is:

C) The y-intercept will always be the vertex.

Explanation:

If b=0, this changes our function to:
f(x) = ax²+0x+c
f(x) = ax²+c

The vertex is first found by finding the axis of symmetry.  This is found using the formula:

x = -b/2a

Since b=0, this gives us:
x = -0/2a = 0

x=0 is the axis of symmetry.

Now we substitute this into the function to find the vertex:
f(x) = a(0)²+c
f(x) = 0+c
f(x) = c

This means (0, c) is the vertex.

For a quadratic function in standard form, c is the y-intercept; this means the y-intercept will be the vertex.

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