Transcript Writing Quadratic Equations given different

Writing Quadratic
Equations Given
Different Information
By: Melissa Light, Devon Moran,
Christy Ringdahl and Jess Ward
When given roots of a graph, you will have to
use the FOIL method to find the intercept
form.
FOIL Method: First
Outer
Inner
Last
1) (3x)(x) = 3x2
2) (3x)(2) = 6x
3) (1)(x) = 1x = x
4) (1)(2) = 2
Final Answer: 3x2 +7x+2
(6,11), (2,3), (-2,19)
• To solve this, you need to use the standard form of a quadratic
equation which is y=ax^2+bx+c.
• Plug in the x and y values for each point, and get three equations.
• With this system of three equations, solve using one of the
methods you have previously learned, for example elimination of a
variable or substitution.
The equations for each point would be:
1. 11=36a+6b+c
2. 3=4a+2b+c
3. 19=4a-2b+c
In this problem, eliminate ‘c’ in all three equations and solve to get
the a, b, and c values for your final quadratic.
Example: Find the y intercept of
the graph of the following
quadratic functions. F
1. (x) = x2 + 2x - 3
2. h(x) = -x2 + 4x + 4
Solution:
1.f(0) = -3. The graph of f has a y
intercept at (0,-3).
2. h(0) = 4. The graph of h has a
y intercept at (0,4).
y=ax^2+bx+c



a=leading coefficient, determines width of
parabola and whether parabola opens up or down
b=linear coefficient, determines whether the slope
is negative or positive
c=constant, determines how much the graph will
be shifted up or down

When given three points on a graph you can use
those to write the standard form of a quadratic
equation.
When given the points (-1,1), (-3,1), and (-4, 4) on a graph you can use them to write the standard form by doing these
steps.
Substitute the values of the points into the standard form equation, ax^2+bx+c.
1=1a-1b+c
1=9a-3b+c
4=16a-4b+c
Then you can put these numbers into a matrix to find what the values of the coefficients are.
When putting these in a matrix the matrix must be 3x4. The top row should be [1 -1 1 1], the middle row should be [9 3 1 1] and the bottom row should be [16 -4 1 4]. In place of the C there is a 1. And the number to the left of the
equal sign must be moved to the end of the equation before being put in the matrix. When those numbers are put
into the matrix then use the rref( button to solve for the coefficients. After you use that button the matrix should
read
[1 0 0 1]
[0 1 0 4]
[0 0 1 4]
In the first row the first 1 represents the A coefficient and the second 1 is the value of the A coefficient. In the second
row the 1 represents the b coefficient and the 4 represents the value of the b coefficient. And finally in the third
row the 1 represents the C coefficient and the 4 represents the value of it. So the final equation is y=1x^2+4x+4.

When given a quadratic function in intercept form
you can write it in standard form by using the
FOIL method.
y=-(x+4)(x-9) intercept form
y=-(x^2-9x+4x-36) multiply the terms by each
other by using the FOIL method (first, inner,
outer, last)
y=-(x^2-5x-36) combine like terms
y=-x^2+5x+36 use the distributive property
When given a quadratic function in vertex form you
can write it in standard form.
y=3(x-1)^2+8 vertex form
y=3(x-1)(x-1)+8 rewrite (x-1)^2
y=3(x^2-x-x+1)+8 multiply using FOIL method
y=3(x^2-2x+1)+8 combine like terms
y=3x^2-6x+3+8 use distributive property
y=3x^2-6x+11combine like terms
y=a(x-p)(x-q)
p,q =p and q are the x-intercepts
The axis of symmetry is halfway between (p,0) and
(q,0).
When you are given the x-intercepts and another
given point on the graph of an equation you can use
the points to write the intercept form of the
equation.
The x-intercepts are (-2,0) and (3,0). The other
point is (-1,2)
y=a(x+2)(x-3) substitute values for p & q
2=a(-1+2)(-1-3) substite values for other point
2=-4a simplify coefficient of “a”
-1/2=a divide both sides by -4
y=-1/2(x+2)(x-3)