1. Chapter 4 Section 4-10 Writing Equations:
1. Vertex Point plus another Point
2. Quadratic Regression

2. Objectives
I can write the equation of a quadratic function given the vertex and another point
I can find the equation to any quadratic function given at least 3 points

3. Vertex Format
Recall that vertex format for any quadratic equation is given by:
y = a (x – h)2 + k
Where (h, k) is the vertex point

4. Finding the Equation
If we know the vertex of a parabola, then we know h and k
Then if we know any other point, we know an x and y value, so we can solve for “a” in the equation

5. Writing an Equation in Vertex Format

6. Example 1
Find the equation of the parabola with vertex (3, -4) and goes through point (0, 1)
y = a(x – h)2 + k
There are 5 variables here: a, h, k, x, y
We know 4 of the 5, so we can solve for “a”

7. Vertex (3, -4) and Point (0, 1)

8. Vertex (3, 1) and Point (6, 3)

9. Example 3
Write the equation in Standard Vertex Format for the parabola that passes thru point (2, 1) and has a vertex point (-2, -3)
y = a(x – h)2 + k
1 = a(2 - -2)2 + -3
1 = a(4)2 – 3
1 = 16a – 3
4 = 16a
a = 1/4

10. Example 4
Write the equation in Standard Vertex Format for the parabola that passes thru point (-3, -5) and has a vertex point (4, 1)
y = a(x – h)2 + k
-5 = a(-3 - 4)2 + 1
-5 = a(-7)2 + 1
-5 = 49a + 1
-6 = 49a
a = -6/49

11. Quadratic Regression
If we know 3 points on a parabola, then we can use quadratic regression and find the equation using the calculator
Given we know the following 3 ordered pairs that are on the parabola
(1, 2), (4, 3), and (7, 6)
Write the equation : y = ax2 + bx + c

12. STAT Button
3rd row
3rd button

13. Entering Data

14. STAT Button
3rd row
3rd button

15. Calculating the Equation

16. Possible Errors Enter wrong number into L1 or L2
Forget a negative sign
Forget to clear L1 or L2
Use a list other than L1 and L2

17. Example 1
Find the equation of the parabola that passes through the following points
(-1, -1), (1, 11), (3, 7)
STAT
EDIT
Enter the L1 data {-1, 1, 3}
Enter L2 data {-1, 11, 7}
Now STAT to Calc #5 Quad Reg then ENTER
y = -2x2 + 6x + 7

18. Homework
WS 6-5