Quadratic Functions

What is the standard form of Quadratic Functions?

• x = ax² + bx + c

• f(x) = ax² + bx + c

• f(x) = a + b + c

• f(x) = ax² + bx + c

What is the vertex of f(x) = -4x²?

• (0, 0)

• (0, -4)

• (0, 4)

• (4, 4)

Answer explanation

The vertex of f(x) = -4x² is (0, 0) because ALL functions with the form of f(x) = ax² will always have a vertex of (0, 0).

What is the axis of symmetry of f(x) = 8x²?

• none of the above

• 8

• -8

• 0

Answer explanation

The axis of symmetry of f(x) = 8x² is 0 because ALL functions with the form of f(x) = ax² will always have an axis of symmetry of 0.

A parabola that opens upward will have what kind of value?

• Average

• Minimum

• Maximum

Answer explanation

"Average" isn't a value, by the way. There are only MINIMUM and MAXIMUM values.

Which one of these set functions is a function?

• f = {(1, 1), (2, 1), (1, 3), (4, 6)}

• f = {(1, 3), (3, 8), (2, 5), (8, 8)}

• f = {(1, 2), (1, 5), (1, 6), (1, 8)}

• f = {(2, 3), (4, 9), (2, 5)}

Answer explanation

A set function is a function when x does not repeat (regardless if y repeats or not).

example: f = {(1, 3), (3, 8) (2, 5), (8, 8)} is a function because the value of each x is different and does not repeat.

while f = {(1, 1), (2, 1), (1, 3), (4, 6)} is not a function because 1 repeats as an x value.

 

What is the shape of the graph of a quadratic function?

• Circle

• U-shaped

• V-shaped

• Heart

Answer explanation

The graph of a quadratic function is a U-shaped curve called a PARABOLA.

A parabola that opens downward will have what kind of value?

• Minimum

• Maximum

What is the vertex of f(x) = x² + 2?

• (0, -2)

• (0, 0)

• (0, 2)

• (2, 0)

Answer explanation

The vertex of f(x) = x² + 2 is (0, 2) because ALL functions with the form of f(x) = x² + k will always have a vertex of (0, k).

In this case, since the value of k is 2, the function's vertex is (0, 2).

For example, the function x² + 8 has a vertex of (0, 8) since the value of k is 8.

What is the axis of symmetry of f(x) = x² + 3?

• 3

• -3

• 0

• 1

Answer explanation

The axis of symmetry of f(x) = x² + 3 is 0 because ALL functions that have the form of f(x) = x² + k will always have an axis of symmetry of 0.

What is the minimum value of f(x) = x² + 4?

• 0

• 4

• -4

• 1

Answer explanation

The minimum value of f(x) = x² + 4 is 0 because since its vertex is (0, 4), the value it will take as its minimum value is 4 since it is the value of y when based on (x, y).

For example, the minimum value of f(x) = 4x² is 0 since its vertex is (0, 0).

The value of y is 0, therefore the minimum value of the function is 0.

Remember: A function's minimum/maximum value is always based on the second number or the value of y in its vertex.