# Algebra II : Quadratic Functions

## Example Questions

### Example Question #11 : Parabolic Functions

Find the location of the vertex of the parabola:

Explanation:

Multiply the two through the binomial.

Now that this is in the order of the polynomial , we can use the vertex formula.

Substitute the known coefficients.

### Example Question #12 : Parabolic Functions

Find the location of the vertex for the parabola.  Is it a max or min?

Explanation:

The polynomial is written in the form of:

This is the standard form for a parabola.

Write the vertex formula, and substitute the known values:

The vertex is at:

Since the coefficient of  is negative, the curve will open downward, and will have a maximum.

### Example Question #13 : Parabolic Functions

A particular parabola has it's vertex at , and an x-intercept at the origin. Determine the equation of the parabola.

None of these

Explanation:

General parabola equation:

Vertex formula:

Where is the value at the vertex.

Combining equations:

Plugging in values for vertex:

Solving for :

Returning to:

combining equations:

Plugging in values of given intercept:

Solving for

Plugging in value:

Plugging in values for the vertex:

Final equation:

### Example Question #1 : Parabolic Functions

Which of the following functions represents a parabola?

Explanation:

A parabola is a curve that can be represented by a quadratic equation.  The only quadratic here is represented by the function , while the others represent straight lines, circles, and other curves.

### Example Question #14 : Parabolic Functions

What is the point of the vertex of the parabola ?  Is it a maximum or minimum?

Explanation:

It is not necessary to FOIL the binomial in order to solve for the vertex.  Switch the terms of the quantity , and this equation will be in vertex form:

Set the inner quantity equal to zero.

Subtract three on both sides.

Divide by negative two on both sides.

The location of the vertex is at .

To determine the point, substitute the value  back to the original equation.

The point of the vertex is at:

Since this parabola opens upward, the point of the vertex will be a minimum.

### Example Question #15 : Parabolic Functions

Where is the vertex located for the given function?

Explanation:

Write the vertex formula.

The given equation is already in standard polynomial form.

Substitute the known values into the formula.

Substitute this value back into the original equation to determine the y value.

Simplify this expression.

The vertex is located at:

### Example Question #16 : Parabolic Functions

Which of these functions represent a parabola?

Explanation:

A parabola is a curve that is represented by a quadratic function. In this case, the only answer that qualifies is .  The other answers represent straight lines, and other types of curves.

### Example Question #17 : Parabolic Functions

Where is the vertex located for   ?

Explanation:

Rewrite the equation in standard polynomial form.

Write the vertex formula and substitute the known coefficients.

The x-value of the vertex is .

Substitute this value back to the original equation.

The vertex is located at:

### Example Question #18 : Parabolic Functions

Determine the vertex given the function:

Explanation:

The parabola is provided in the form of .

Notice that the variable  in this equation is zero.

This means that:

Substitute this value back into the original equation  to determine the y-value.

The vertex is located at:

### Example Question #3 : Graphing Quadratic Functions

All of the following are equations of down-facing parabolas EXCEPT:

Explanation:

A parabola that opens downward has the general formula

,

as the negative sign in front of the  term makes flips the parabola about the horizontal axis.

By contrast, a parabola of the form rotates about the vertical axis, not the horizontal axis.

Therefore, is not the equation for a parabola that opens downward.