IXL - Solve a system of linear and quadratic equations by graphing: parabolas (Geometry practice)

Solve the system of equations by graphing. First graph the equations, and then identify the solutions.

(

–

)

To graph a linear equation, click to plot points on the graph. To graph a quadratic equation, click to plot the vertex first, then plot another point on the graph.

Linear

Quadratic

Edit

Linear

Quadratic

Edit

What are the solutions to the system of equations? Select all that apply.

(

)

(

)

(

)

(

)

There are no solutions.

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Learn with an example

question

Solve the system of equations by graphing. First graph the equations, and then identify the solutions.

(

–

)

–

To graph a linear equation, click to plot points on the graph. To graph a quadratic equation, click to plot the vertex first, then plot another point on the graph.

Linear

Quadratic

Edit

What are the solutions to the system of equations? Select all that apply.

(

)

(

)

(

–

)

(

)

There are no solutions.

key idea

The slope-intercept form of a linear equation is

where

is the slope and

is the

-intercept.

The vertex form of a quadratic equation is

(

–

)

where

(

)

is the vertex of the parabola and

determines the width.

solution

To solve the system of equations, graph both equations and find the points where the graphs intersect.

First, graph the parabola given by the quadratic equation

(

–

)

which is in vertex form. Find the vertex.

(

–

)

(

–

)

The vertex is

(

)

Now, find another point on the parabola by plugging in a different value for

For example, plugging in

is a good choice since it will result in an integer value for

(

–

)

(

)

The result is

So,

(

)

is another point on the parabola.

Graph the parabola with vertex

(

)

that passes through

(

)

Next, graph the line

–

which is in slope-intercept form. Find the slope and

-intercept.

–

The

-intercept

–

So,

(

–

)

is a point on the line.

The slope is

Move up 3 and right 5 to find another point on the line,

(

)

Graph the line that passes through

(

–

)

and

(

)

Now, find the points where the graphs intersect.

The graphs of the equations do not intersect.

So, the system of equations has no

solutions.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.9Graph parabolas

O.14Solve a system of equations using any method

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