Chapter 4
Section 4-10
Writing Equations:
1. Vertex Point plus another Point
2. Quadratic Regression
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
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
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
Writing an Equation in Vertex Format
y  a ( x  h)  k
2
Po int : ( x, y )
Vert ex: (h, k )
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”
Vertex (3, -4) and Point (0, 1)
y  a ( x  h)  k
5
2
1  a(0  3)  4 a 
9
1  9a  4
5
2
y  ( x  3)  4
5  9a
9
2
7
Vertex (3, 1) and Point (6, 3)
y  a ( x  h)  k
2
2
3  a(6  3)  1 a 
9
3  9a  1
2
2
y
8
9
( x  3)  1
2
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
2
y  ( x  2)  3
• 1 = 16a – 3
4
• 4 = 16a
• a = 1/4
9
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
6
2
y   ( x  4)  1
• -5 = 49a + 1
49
• -6 = 49a
• a = -6/49
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
STAT Button
• 3rd row
• 3rd button
Entering Data
STAT Button
• 3rd row
• 3rd button
Calculating the Equation
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
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
Homework
• WS 6-5