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

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

4. The parabola will open down when the a is negative. The parabola will open up when the a is positive. The standard form of a quadratic function is: y = ax 2 + bx + c a > 0 a < 0

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

6. For example, find the line of symmetry of y = 3x 2 – 18x + 7 How do we find the Line of Symmetry? Given that a function is in the form: The equation of the line of symmetry is y = ax 2 + bx + c

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 = ax 2 + bx + c STEP 1: Find the line of symmetry. STEP 2: Plug the x – value into the original equation to find the y value. y = 3x 2 – 18x + 7

8. A Quadratic Function in Standard Form There are 3 steps to graphing a parabola in standard form. STEP 1: Find the line of symmetry STEP 2: Find the vertex STEP 3: Find two other points and reflect them across the line of symmetry. Then connect the five points with a smooth curve.

9. STEP 1: Find the line of symmetry y = 2x 2 – 4x – 1 A Quadratic Function in Standard Form

10. STEP 2: Find the vertex A Quadratic Function in Standard Form y = 2x 2 – 4x – 1

11. STEP 3: Find two other points and reflect them across the line of symmetry. Then connect the five points with a smooth curve. y = 2x 2 – 4x – 1 A Quadratic Function in Standard Form

12. You try! STEP 1: Find the line of symmetry STEP 2: Find the vertex STEP 3: Find two other points and reflect them across the line of symmetry. Then connect the five points with a smooth curve. y = -2x 2 – 4x + 3