1. Quadratic Functions Graphs
In Standard Form

2. Graphing Quadratic Functions
Quadratic functions have the form: y = ax2 + bx + c When we graph them, they make a parabola!

3. Vertex of a Parabola A parabola can open up or down.y x
The vertex of a parabola is the highest or lowest point of the parabola.
Vertex

4. y = ax2 + bx + c The standard form of a quadratic function is:
The parabola will open up when the a is positive.
a < 0
a > 0
The parabola will open down when the a is negative.

5. The line of symmetry ALWAYS passes through the vertex.
If we drew a line down the middle of the parabola, we call this line the line of symmetry. y x
The line of symmetry ALWAYS passes through the vertex.

6. How do we find the Line of Symmetry?
Given that a function is in the form:
For example, find the line of symmetry of
y = 3x2 – 18x + 7
y = ax2 + bx + c
The equation of the line of symmetry is

7. How do we find the vertex?
We know that the vertex is a coordinate (x, y). If we know the line of symmetry, we know the x coordinate! Now we, just plug x into
to find the y coordinate.
y = 3x2 – 18x + 7
STEP 1: Find the line of symmetry.
y = ax2 + bx + c
STEP 2: Plug the x – value into the original equation to find the y value.

8. A Quadratic Function in Standard Form
There are 5 steps to graphing a parabola in standard form.
STEP 1: Find the axis of symmetry using
STEP 2: Find the vertex: ( , plug in )
STEP 3: Find the y-intercept (value of c)
STEP 4: Plot the matching or symmetrical point
STEP 5: Sketch your curve

9. A Quadratic Function in Standard Form
y = 2x2 – 4x – 1 y x
STEP 1: AOS
STEP 2: vertex
STEP 3: y-intercept
STEP 4: symmetrical point
STEP 5: graph parabola

10. You try!
y = -2x2 – 4x + 3 y x