1. Graphing Quadratic Equations in Vertex and Intercept Form
Section 4.2
Graphing
Quadratic Equations in Vertex and Intercept Form

2. The y intercept of the graph is c if the equation is in STANDARD FORM
Quadratic Functions
A quadratic function has the form: f (x) = ax2 + bx + c
Where a, b and c are real numbers and
a is not equal to 0.
The y intercept of the graph is c if the equation is in STANDARD FORM .
The basic shape of the graph is a PARABOLA
or U shaped

3. Positive Quadratic
Negative Quadratic
y = ax2
y = -ax2
Parabolas always have a lowest point (minimum) or a highest point (maximum, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex".

4. Vertex- Axis of symmetry- The lowest or highest point of a parabola.
The vertical line through the vertex of the parabola.
Axis of
Symmetry

5. Vertex Form: y = a(x – h)2 + k, - the vertex is the point (h, k).
- the axis of symmetry is x = h
- if “a” is positive it opens up
- if “a” is negative it opens down
Plot the vertex and then find two other points by using “a” as your rise/run

7. Vertex Form (x – h)2 + k – vertex form
Each function we just looked at can be written in the form (x – h)2 + k, where (h , k) is the vertex of the parabola, and x = h is its axis of symmetry.
(x – h)2 + k – vertex form
Equation
Vertex
Axis of Symmetry
y = x2 or y = (x – 0)2 + 0
(0 , 0)
x = 0
y = x2 + 2 or y = (x – 0)2 + 2
(0 , 2)
y = (x – 3)2 or y = (x – 3)2 + 0
(3 , 0)
x = 3

8. (-2, 5) EXAMPLE A Graph a quadratic function in vertex form 12
Graph y = – (x + 2)2 + 5.
SOLUTION
STEP 1: Identify the vertex
(-2, 5)
STEP 2: Plot the vertex & draw
the line of symmetry
STEP 3: Determine if it opens up or down

9. EXAMPLE A
Graph a quadratic function in vertex form 12
Graph y = – (x + 2)2 + 5.
STEP 4: Use “a” as your rise/run
Down 1 and over 2
STEP 5: Draw a parabola

12. Example B: Graph y = (x + 2)2 + 1
Analyze y = (x + 2)2 + 1.
Step 1 Plot the vertex (-2 , 1)
Step 2 Draw the axis of symmetry, x = -2.
Step 3 Find and plot two points on one side , such as (-1, 2) and (0 , 5).
Step 4 Use symmetry to complete the graph, or find two points on the
left side of the vertex.

13. Example C: Graph y=-.5(x+3)2+4
a is negative (a = -.5), so parabola opens down.
Vertex is (h,k) or (-3,4)
Axis of symmetry is the vertical line x = -3
Table of values x y
-1 2
-3 4
-5 2
Vertex (-3,4)
(-4,3.5)
(-2,3.5)
(-5,2)
(-1,2)
x=-3

14. Now you try one!

15. Minimum “a” is positive Maximum “a” is negative
GUIDED PRACTICE
for Examples 1 and 2
Graph the function. Label the vertex and axis of symmetry.
y = (x + 2)2 – 3
Minimum “a” is positive
y = –(x + 1)2 + 5
Maximum “a” is negative

20. Intercept Form Equation
y=a(x-p)(x-q)
The x-intercepts are the points (p,0) and (q,0).
The axis of symmetry is the vertical line x=
The x-coordinate of the vertex is
To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y.
If “a” is positive, parabola opens up
If “a” is negative, parabola opens down.

22. Example D: Graph y=-(x+2)(x-4)
Since a is negative, parabola opens down.
The x-intercepts are
(-2,0) and (4,0)
To find the x-coord. of the vertex, use
To find the y-coord., plug 1 in for x.
Vertex (1,9)
The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex)
(1,9)
(-2,0)
(4,0)
x=1

27. Now you try one! y=2(x-3)(x+1) Open up or down? X-intercepts? Vertex?
Axis of symmetry?

28. x=1
(-1,0)
(3,0)
(1,-8)