Quadratic Functions

Quadratic Functions

Graphs of Quadratic Functions

• Is called a parabola

• If the coefficient of x² is positive, the parabola open upward

• If the coefficient of x² is negative the parabola opens downward

Multiple Choice

What would be an example of a quadratic equation?

• x+5

• x³+2x²+5x-2

• x²+3x-10

The vertex (or turning point) of the parabola is the lowest point on the graph when it opens upward and the highest when it opens downward.

Multiple Choice

is the lowest or highest point of the parabola

• vertex

• axis

• equation

• symmetry

Multiple Choice

Does this graph in the back have maximum or minimum value?

• maximum
• minimum
• neither
• both

The standard form of a quadratic equation

f(x)=a(x-h)²+k, where the vertex is (h,k)

If a is positive, the parabola open upward but if a is negative it opens downward

Multiple Choice

In the function f(x)=2(x+5)²-8, the parabola opens

• upward

• downward

Multiple Choice

In the function f(x)=-5(x+3)²-8, the parabola opens:

• upward

• downward

Finding the vertex of a parabola in standard form

In the function f(x)=(x+1)²-2, the vertex is (-1,-2)

*change the sign of h, k remains the same

In the function f(x)=-2(x-1)²+3, the vertex is (1,3)

• change the sign of h

• the sign of k remain the same

Multiple Choice

If given the equation
y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5, -4)
• (-5, -4)
• (-15, -4)
• (15, -4)

Multiple Choice

Identify the vertex and whether the graph opens up or down.

• (-1, 4); opens up
• (-1, 4); opens down
• (1, 4); opens up
• (1, 4); opens down