# Algebra 1 : How to graph a quadratic function

## Example Questions

### Example Question #1 : How To Graph A Quadratic Function

What is the minimum possible value of the expression below?  The expression has no minimum value.    Explanation:

We can determine the lowest possible value of the expression by finding the -coordinate of the vertex of the parabola graphed from the equation . This is done by rewriting the equation in vertex form.    The vertex of the parabola is the point .

The parabola is concave upward (its quadratic coefficient is positive), so represents the minimum value of . This is our answer.

### Example Question #6 : Graphing Parabolas

What is the vertex of the function ? Is it a maximum or minimum? ; minimum ; maximum ; minimum ; maximum ; minimum

Explanation:

The equation of a parabola can be written in vertex form: .

The point in this format is the vertex. If is a postive number the vertex is a minimum, and if is a negative number the vertex is a maximum. In this example, . The positive value means the vertex is a minimum.  ### Example Question #4 : Graphing Polynomial Functions

Which of the graphs best represents the following function?    None of these  Explanation: The highest exponent of the variable term is two ( ). This tells that this function is quadratic, meaning that it is a parabola.

The graph below will be the answer, as it shows a parabolic curve. ### Example Question #2 : How To Graph A Quadratic Function

What is the equation of a parabola with vertex and -intercept ?      Explanation:

From the vertex, we know that the equation of the parabola will take the form for some .

To calculate that , we plug in the values from the other point we are given, , and solve for :      Now the equation is . This is not an answer choice, so we need to rewrite it in some way.

Expand the squared term: Distribute the fraction through the parentheses: Combine like terms: ### Example Question #8 : Graphing Polynomial Functions      None of the above    Explanation:

Starting with  moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .

### Example Question #1 : How To Graph A Quadratic Function

Which of the following graphs matches the function ?      Explanation:

Start by visualizing the graph associated with the function : Terms within the parentheses associated with the squared x-variable will shift the parabola horizontally, while terms outside of the parentheses will shift the parabola vertically. In the provided equation, 2 is located outside of the parentheses and is subtracted from the terms located within the parentheses; therefore, the parabola in the graph will shift down by 2 units. A simplified graph of looks like this: Remember that there is also a term within the parentheses. Within the parentheses, 1 is subtracted from the x-variable; thus, the parabola in the graph will shift to the right by 1 unit. As a result, the following graph matches the given function :  