Introduction to Graphing Parabolas

Graphing Quadratics in Standard Form

 $y=ax^2+bx+c$  

• if a is positive, the parabola opens upward and has a minimum

• if a is negative, the parabola opens downward and has a maximum

Multiple Choice

$$y=-2x^2+3x-7$$  
This parabola opens...

• Upward

• Downward

Multiple Choice

$$y=-4x^2-2x+8$$  
This parabola has a...

• Minimum

• Maximum

Finding the Vertex

• Use the formula to find the x-value.  $x=-\frac{b}{2a}$  

• Example:  $y=2x^2-12x-8$  

•  $x=-\frac{\left(-12\right)}{2\left(2\right)}=\frac{12}{4}=3$  

Multiple Choice

$$y=2x^2-8x+10$$  Find the x-coordinate of the vertex.

• $$x=2$$  

• $$x=-2$$  

• $$x=\frac{1}{4}$$  

• $$x=-4$$  

Multiple Choice

Given that the x-coordinate of the vertex is 2, what is the axis of symmetry?

• $$x=-2$$

• $$\left(2,0\right)$$

• $$\left(0,-2\right)$$

• $$x=2$$

Finding the Vertex

• Use the formula to find the x-value.  $x=-\frac{b}{2a}$  

• Once you have found the x-value, substitute in to the original equation find the corresponding y-value.

• Ex:  $y=2x^2-12x-8$  where  $x=3$ 
  

•  $y=2\left(3\right)^2-12\left(3\right)+8=18-36+8=-10$  

• So the vertex is (3,-10)

Multiple Choice

Given that the x-coordinate of the vertex is 2, what is the y-coordinate of this equation?   $$y=2x^2-8x+10$$  

• $$y=0$$  

• $$y=2$$  

• $$y=-4$$  

• $$y=18$$  

Multiple Choice

$$y=-x^2+6x+5$$  

Find the vertex.

• (4,-3)

• (-3,-22)

• (-4,3)

• (3, 14)

Finding the y-intercept

• The y-intercept is at (0,c)

• Example:  $y=4x^2+8x-5$  

• (0,-5)

Multiple Choice

$$y=3x^2-5x+7$$  

Find the y-intercept

• (0,7)

• (7,0)

• (0,-5)

• (5,0)

Finding x-intercepts

• You find the x-intercepts by factoring, using the quadratic formula, or completing the square.