Algebra II 4.1 - 4.3 Review

Algebra II 4.1 - 4.3 Review

Graphing and factoring Quadratics

Graphing Quadratics

• Standard Form: y = ax² + bx + c

• Axis of symmetry:

   $x=-\frac{b}{2a}$  

• Vertex:  The value you found above gives you the x-coordinate, plug in to find y-coordinate.

Multiple Choice

What is the axis of symmetry for the quadratic function:

 $f\left(x\right)=-3x^2+12x-13$  

*Remember to use the equation x = -b/2a*

•  $x=18$  
  

•  $x=-2$  
  

•  $x=2$  
  

•  $x=-18$  
  

Multiple Select

Choose all the correct properties of the graph of this quadratic function:

 $y\ =\ 3x^2-12x+4$  

• The parabola opens upward.

• The parabola opens downward.

• The axis of symmetry is x = 2.

• The axis of symmetry is x = -18.

• The y-intercept is (0, 4).

Multiple Choice

Graph the quadratic function:

g(x) = 2x² - 12x + 16

Multiple Choice

What is the vertex of the parabola?

f(x) = -3x² + 12x - 13

*You found the AOS for this one a few questions ago*

• (2, -1)

• (-2, -49)

• (-18, -1021)

• (18, -769)

Vertex Form of a Quadratic

• y = a(x - h)² + k

• Vertex: (h, k)

• Axis of Symmetry: x = h

Multiple Choice

What is the vertex of the quadratic function?

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

*Think (h, k)*

• (-2, 2)

• (2, -2)

• (2, 2)

• (-2, -2)

Multiple Choice

What is the axis of symmetry for the graph of the quadratic function shown?

 $y=-\left(x-1\right)^2+4$  

• x  = -1

• x = 1

• x = -4

• x = 4

Multiple Choice

Graph the quadratic function:

 $f\left(x\right)=-\left(x+3\right)^2+4$  

Multiple Choice

What is the minimum value for the graph of the quadratic function?

 $y=3\left(x+2\right)^2-5$  

• 3

• -2

• 4

• -5

Factoring Quadratics

• GCF - Greatest Common Factor

• Reverse FOIL Method

• Solving by Factoring

Multiple Choice

Factor the quadratic expression:

 $6x^2-3x$  

•  $6\left(x^2-3x\right)$  

•  $3x^2\left(2x-1\right)$  

•  $3x\left(2x-1\right)$  

•  $2x\left(3x+1\right)$  

Multiple Choice

Factor the quadratic expression:

 $x^2+2x-35$  

• (x +7)(x + 2)

• (x + 7)(x + 5)

• (x - 7)(x + 5)

• (x + 7)(x - 5)

Multiple Choice

What are the solutions to the equation (Hint: Factor to solve)?

 $x^2+2x-35=0$  

• {-8, 0}

• {4, 2}

• {5, -7}

• {-7, -4}

Multiple Choice

Solve by factoring:

 $p^2-3p=0$  

• {0, 3}

• {0, -3}

• {0}

• no solution

Open Ended

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