Graphing Quadratics in Standard Form

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.