IXL - Solve a system of quadratic equations by graphing: parabolas (Algebra 2 practice)

Solve this system of equations by graphing.

(

)

–

(

–

)

For each equation, click to plot the vertex first. Then plot another point on the graph.

(

)

–

(

–

)

(

)

–

(

–

)

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

(

)

(

)

(

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)

There are no real solutions.

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Learn with an example

question

Solve this system of equations by graphing.

(

–

)

–

(

–

)

–

For each equation, click to plot the vertex first. Then plot another point on the graph.

(

–

)

–

(

–

)

–

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

(

–

)

(

–

)

(

–

)

There are no real solutions.

key idea

There are two common forms of a quadratic function.

Vertex form:

(

–

)

Standard form:

In vertex form, the parabola's vertex is

(

)

In standard form, the

-coordinate

of the parabola's vertex is

–

solution

You were asked to solve this system of equations by graphing.

(

–

)

–

(

–

)

–

Graph the first equation.

The first equation,

(

–

)

–

is in vertex form. You can rewrite it as

(

–

)

–

to see that

and

–

So, the vertex is

(

–

)

To find another point on the parabola, pick a nearby

-value,

such as

Substitute this value into

(

–

)

–

to find the corresponding

-value.

Substitute

(

–

)

–

Substitute

Simplify

(

)

–

Simplify

–

So, the point

(

–

)

is also on the parabola. Plot both points to graph the parabola.

(

)

(

)

Graph the second equation.

The second equation,

(

–

)

–

is also in vertex form. So, you can repeat the same steps. First, rewrite it as

(

–

)

–

to see that

and

–

So, the vertex is

(

–

)

To find another point on the parabola, pick a nearby

-value,

such as

Substitute this value into

(

–

)

–

to find the corresponding

-value.

Substitute

(

–

)

–

Substitute

Simplify

(

)

–

Simplify

–

So, the point

(

–

)

is also on the parabola. Plot both points to graph the parabola.

(

)

(

)

Solve the system of equations.

To solve the system of equations, find the point of intersection.

(

)

The parabolas appear to intersect at the point

(

–

)

You can check this solution by substituting

and

–

into the original equations.

Equation 1:

(

–

)

–

≟

(

–

)

–

Equation 2:

(

–

)

–

≟

(

–

)

–

Each equation simplifies to the true statement

–

So, the solution to the system of equations is

(

–

)

$Confetti$

Excellent!

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P.1Solve a system of linear and quadratic equations by graphing: parabolas

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