5.1 Graphing Quadratic Functions
A quadratic function has the form y = ax 2 + bx + c where a ≠ 0. The graph of a quadratic
function is called a parabola.
The lowest/highest point on the graph of a quadratic function is called the vertex.
The axis of ssymmetry
ymmetry for the graph of a quadratic function is the vertical line through the
vertex.
• The y-intercept is c. So the point (0, c) in on the parabola.
Graphing Parabolas in Standard Form: y = ax 2 + bx + c
1.) Locate the x−coordinate of the vertex by solving −
b
2a
2.) Plug the x−coordinate back into the original equation to solve for the
y−coordinate of the vertex.
3.) Plot the vertex.
4.) Choose convenient values for x to the left and right of the vertex to determine
additional points on the graph. Plug those values into the equation to solve for y.
5.) Connect with a smooth curve.
Ex:
Ex:
y = 2x 2 − 8x + 6
a =____ b =____ c =____
vertex: ____________
axis of symmetry: __________
y-intercept: _____________
factor to find x-intercept:
x
y
Ex:
Ex:
y = −x 2 + x + 12
x
y
x
y
a =____ b =____ c =____
vertex: ____________
axis of symmetry: __________
y-intercept: _____________
factor to find x-intercept:
Ex:
1
2
y = x2 −8
a =____ b =____ c =____
vertex: ____________
axis of symmetry: __________
y-intercept: _____________
factor to find x-intercept:
Minimum & Maximum Values
For y = ax 2 + bx + c , the vertex’s y−coordinate is the minimum value of the function
if a > 0 and the maximum value if a < 0.
Intercept Form:
Form y = a( x − p )( x − q )
1.) Locate the x−intercepts. The x−intercepts are at “p” and “q”. Because of the
subtraction sign in the Intercept Form, you can simply find the opposite of the
numbers for p and q in the equation.
For example: for y = ( x + 1)( x − 7) , the intercepts are x = −1 and x = 7.
2.) Plot the x−intercepts on the x−axis.
3.) Find the average of the two intercepts, which will be the x−coordinate of the
vertex. Substitute the x−value for the vertex into the equation to find the
y−coordinate. Plot that point.
4.) Connect with a smooth curve.
Ex:
1
2
y = − (x − 2)(x + 4)
x
y
x
y
a =____ b =____ c =____
vertex: ____________
axis of symmetry: __________
y-intercept: _____________
x-intercepts:
Ex:
Ex:
y = (x + 1)(x − 5)
a =____ b =____ c =____
vertex: ____________
axis of symmetry: __________
y-intercept: _____________
x-intercepts: