# Algebra 1 : How to use the quadratic function

## Example Questions

### Example Question #1 : How To Use The Quadratic Function

Solve the equation:

Explanation:

To solve the quadratic equation, , we set the equation equal to zero and then factor the quadratic, . Because these expressions multiply to equal 0, then it must be that at least one of the expressions equals 0. So we set up the corresponding equations  and      to obtain the answers  and

### Example Question #2 : Quadratic Formula

Solve for :

The solution is undefined.

Explanation:

To factor this equation, first find two numbers that multiply to 35 and sum to 12.  These numbers are 5 and 7.  Split up 12x using these two coefficients:

### Example Question #1 : How To Use The Quadratic Function

Given , find .

Explanation:

Plug in a for x:

Next plug in (a + h) for x:

Therefore f(a+h) - f(a) =  .

### Example Question #2 : How To Use The Quadratic Function

Which of the following is the correct solution when    is solved using the quadratic equation?

Explanation:

### Example Question #3 : How To Use The Quadratic Function

Give the minimum value of the function .

This function does not have a minimum.

Explanation:

This is a quadratic function. The -coordinate of the vertex of the parabola can be determined using the formula , setting :

Now evaluate the function at :

### Example Question #4 : How To Use The Quadratic Function

Quadratic equations may be written in the following format:

In the equation ,  what is the value of ?

Explanation:

when using the quadratic formula, your variables are as follows

For the given equation below:

The values of each coefficient are:

### Example Question #4 : How To Use The Quadratic Function

Solve for x.

Explanation:

The quadratic formula is as follows:

We will start by finding the values of the coefficients of the given equation, but first we must simplify.

Move all the terms to one side and set the equation equal to .

Rearrange.

We can then find the values of the coefficients of the equation:

Quadratic equations may be written in the following format:

In our case, the values of the coefficients are:

Substitute the coefficient values into the quadratic equation:

After simplifying we are left with:

### Example Question #6 : How To Use The Quadratic Function

Solve for :

Explanation:

To find , we must factor the quadratic function:

Solve for :