Solve Quadratics by Graphing

Solve Quadratics by Graphing

By Michelle Wilson

Remember, x-intercepts can be called solutions, roots, and zeros as well.

Solutions are where y = 0 once you get the equation to equal zero.​

​

​Types of solutions

​The Solutions are the

x-intercept

​

​NOTE: To solve a Quadratic (or any) equation by graphing, you must first get the equation equal to zero and in Standard Form.

​We can use Desmos to see the x-intercepts on the graph and in the table of values.

​

Make sure the equation is equal to zero and then you can replace

0 = equation

with

y = ​equation

Multiple Select

What are the various names we use to describe all "solutions" to a Quadratic Function?

Select all correct terms as given in these notes.

• roots

• zeros

• x-intercepts

• y-intercepts

• origin

Multiple Choice

Set $$8x^2-6x=-7$$  equal to zero

Tip: Keep the leading term (x²) positive

• $$8x^2-6x-7=0$$  

• $$8x^2+6x+7=0$$  

• $$8x^2-6x+7=0$$  

• $$8x^2+6x-7=0$$  

Multiple Choice

Set $$5x+3=7x^2-x+4$$  equal to zero

Tip: Keep the leading term (x²) positive

• $$7x^2-6x+1=0$$  

• $$7x^2-4x+7=0$$  

• $$7x^2-6x+1$$  

• $$7x^2+4x+7=0$$  

Multiple Select

How should I write $$2x+4x^2=-6x+12$$   in Desmos so that I can graph or use a table?

Select ALL that can be graphed in our Desmos State Test Calculator.

• $$4x^2+8x+12=0$$  

• $$4x^2+8x+12$$  

• $$y=4x^2+8x-12$$  

• $$2x+4x^2=-6x+12$$  

Multiple Select

Solve $$y=4x^2+8x-12$$  

• x = -3

• x = -2

• x = -1

• x = 0

• x = 1

​How did you do?

​2 Solutions

x = -3 or x = 1

Make sure you are writing examples down in your notes!

Any Questions before you solve more?

Multiple Choice

What  are the solutions of this graph?

• -2 and 3

• -1/2 and -6

• -2 and -6

• 3 and -6

Multiple Choice

What is another word that describes the zeros of a quadratic function?  

• y-intercepts

• vertex

• x-intercepts

• maximum

Multiple Choice

How many zeros does this parabola have? 

• 3

• 2

• 0

• 1

Multiple Choice

The solutions to y= 2x² - x - 3 are...

• 1 and 1.5

• -1 and 1.5

• -1 and -1.5

• 1 and -1.5

Multiple Choice

What should you do first in solving this equation?
x² + 6x - 13 = 3

• Get factored form

• Write down: a=1, b=6, c=-13

• Make it equal 0 by subtracting 3 on each side

• Type it all in a calculator.

Multiple Choice

Solve

x² + 44 = -15x

TIP: Writing a set of numbers, using braces, like {1, 2}

is the same as listing them separately x = 1 or x = 2

• x = {-8, 2}

• x = {-7, 5}

• x = {-11, -4}

• x = {-11}

Multiple Choice

How many solutions does this parabola have?

• 0

• 1

• 2

• 3

Multiple Select

Select the solution(s) for the quadratic:   $$x^2-11x+19=-5$$  

• x = 3

• x = 8

• x = -9

• x = -3

Multiple Select

Solve   $$f\left(x\right)=-x^2-7x-6$$  

• x = 6

• x = -6

• x = 1

• x = -1

• x = 0

In Closing

Make sure to have good notes in your notebook to use when reviewing this lesson.

Make sure to ask any questions you have!

​Solutions (x-intercepts, zeros, roots) can be found by graphing.

To graph a function, we must first get it in Standard Form and equal to zero.

Reminder: We call solutions "zeros", because they are where the function has y equal to zero.