Lecture 9.2 - Solve Quadratic Functions by Graphing

Lecture 9.2 - Solve Quadratic Functions by Graphing

G²

Solve what, bruh?

Solutions to quadratic equations

Solving a quadratic equation means finding solutions that make the equation true. We can do that by setting the function equal to 0, but we can also find solutions by analyzing graphs and finding where y=0.

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Are you down with the ZPP?

seriously, Solve what, bruh?

methods to solving quadratic equations

• Factoring using the Zero Product Property

• Square Root Method (only works when a variable squared can be isolated)

• Graphing - find where the parabola crosses the x-axis​

  • yeah, we're about to do this​

Yeah, you know me.

Fr, seriously, Solve what, bruh?

​Solution scenarios for quadratic equations

​two real solutions

How would you describe the vertex location in each scenario?​

​no real solutions

​one real solution

Multiple Choice

What are the zeros of the parabola? 

• 1, 5
• 3, -5 
• 3, 0
• -6, 1

Multiple Choice

What are the green dots called?

• axis of symmetry
• vertex
• parabola
• roots or x-intercepts

Multiple Choice

Determine the solutions of the graph:

• No Solutions

• (-3, 0) and (-1, 0)

• Infinity Many Solutions

• (-1, 0)

Multiple Choice

What are the solutions?

• x=4

• x= 0

• y=-4

• There are no real solutions

Multiple Choice

How many solutions are there?

• 0

• 1

• 2

• 3

Multiple Choice

What are the solutions?

• x=4

• x= 0

• y=-4

• There are no real solutions

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

Multiple Choice

What are the zeros of the function in the graph?

• (-1, 0) and (1, 0)

• (0, -1) and (0, 1)

• (0, -1)

• (-1, 0) and (1, 0) and (0, -1)

Multiple Select

To solve a quadratic by graphing is to find where the parabola crosses the x-axis. We call these the ___. Select all that apply.

• zeros

• x-intercepts

• solutions

• roots

What if it's already solved, bruh?

writing equations given the solution(s) and another point

To write the equation, a graph with root(s) and one other point is required or simply 2 roots and 1 point as ordered pairs.​

Multiple Choice

Write the equation of the quadratic function that has a x-intercepts at (2, 0) and (4, 0) and passes through the point (3, 4).

• y = -4(x - 2)(x - 4)

• y = -4(x + 2)(x + 4)

• y = 4(x - 2)(x - 4)

• y = -0.25(x - 2)(x - 4)

Multiple Choice

Which quadratic function best represents the graph that has x-intercepts at 9 and 1 and passes through the point (0, -18)?

• y = x² + 9x - 18
• y = -2(x - 9)(x - 1)
• y = -2(x + 9)(x + 1)
• y = 2(x + 9)(x + 1)

Multiple Choice

What is the equation of the parabola?

• y =(x - 1)(x-3)

• y = -1/2(x - 1)(x + 3)

• y = 2(x + 1)(x - 3)

• y = - 1(x- 1)(x - 3)

Multiple Choice

What is the equation for this parabola in factored form?

• y=(x+2)(x-1)
• y=(x-2)(x+1)
• y=(x-2)(x-1)
• y=(x+2)(x+1)

What if it's already in factored form, bruh?

converting factored form to standard form

Once we've written an equation in factored form, we can expand it to standard form. Other terms you may have heard instead of "expand":

• double distribute

• FOIL

• simplify

• reverse factor​

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Don't forget to distribute the 'a' value!

Multiple Choice

Rewrite in standard form: $$y=\left(x+2\right)\left(x+3\right)$$  

• $$y=2x+5$$  

• $$y=x^2+6$$  

• $$y=x^2+x+6$$  

• $$y=x^2+5x+6$$  

Multiple Choice

Rewrite in standard form: $$y=2\left(x-3\right)\left(x+5\right)$$  

• $$y=x^2+2x-15$$  

• $$y=2x^2-30$$  

• $$y=2x^2+2x-15$$  

• $$y=2x^2+4x-30$$  

Multiple Choice

Go from factored to standard form $$\left(x+8\right)\left(3x-2\right)$$  

• $$3x^2+22x-16$$  

• $$3x^2+26x-16$$  

• $$3x^2+22x+6$$  

• $$8x\cdot-6x$$