Alg2CP - Graphing Quadratics

Graphing Quadratics

Alg 2 CP

Remember back to last unit and transformations . . .

Multiple Choice

What steps transform the graph y = x² to y = (x-4)²

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units

Multiple Choice

What steps transform the graph y = x² to y = x² + 8

• shifted up 8 units

• shifted down 8 units

• shifted left 8 units

• shifted right 8 units

Multiple Choice

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

Multiple Choice

What is the equation of this graph?

• f(x) = (x -5)² + 1

• f(x) = (x - 1)² - 5

• f(x) = (x + 1)² - 5

• f(x) = (x + 5)² +1

Vertex Form

 $f\left(x\right)=\left(x-h\right)^2+k$  
has a vertex at  $\left(h,k\right)$  

Multiple Choice

What is the vertex of the graph?

• $\left(0.13\right)$

• $\left(3,4\right)$

Multiple Choice

Given the equation y = (x + 5)² - 4,

what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Multiple Choice

Which equations matches the graph above?

• $h\left(x\right)=\ \left(x+1\right)^2-4$

• $h\left(x\right)=-\left(x+1\right)^2-4$

• $h\left(x\right)=\left(x+4\right)^2-1$

• $h\left(x\right)=-\left(x+4\right)^2+1$

How to Graph Vertex Form

1. Find the vertex from the equation and plot it

2. Choose two x-values near the vertex, plug them into the equation, and find their y-values.

3. Plot the two other points

Ex: Graph  $f\left(x\right)=\left(x-2\right)^2-3$  

.

Try it: Graph  $f\left(x\right)=\left(x+1\right)^2-4$  

.

Refresher: How to Graph Factored Form

1. Find the x-intercepts

2. Find the axis of symmetry

3. Plug the axis of symmetry into the equation to find the vertex

Ex: Graph  $y=\left(x-3\right)\left(x+1\right)$  

.

Try it: Graph  $y=\left(x-8\right)\left(x-2\right)$  

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How to Graph Standard Form

Ex:  $f\left(x\right)=x^2+2x-8$  

You can
1. Factor the equation and graph from factored form
OR
2. Complete the square and graph from vertex form