My math teacher said to use the FOIL (First Outer Inner Last) property to simplify these quadratic equations I have made from looking at two parabolas.
Here are my equations & how would you use the FOIL property on each of the equations and also can someone help me with finding a for the second equation:
y=-15/20.25(x+1.5)^2+0
y=a(x+2)^2+1.5
(x+1.5)(x+1.5) = x^2 + 1.5 x + 1.5 x + (1.5*1.5)
= x^2 + 3 x + 2.25
get it?
So then how would I put it into the original equation, Damon?
To simplify quadratic equations using the FOIL (First Outer Inner Last) property, you generally need to expand and simplify the expressions. Let's go through each equation one by one:
1. y = -15/20.25(x + 1.5)^2 + 0
The expression inside the square, (x + 1.5)^2, represents the "First" term squared. To apply the FOIL property, we need to multiply each part of the binomial by itself:
(x + 1.5)(x + 1.5)
Using the FOIL method, we get:
First: x * x = x^2
Outer: x * 1.5 = 1.5x
Inner: 1.5 * x = 1.5x
Last: 1.5 * 1.5 = 2.25
Combining these terms, we have:
x^2 + 3x + 2.25
Now, multiply this expression by -15/20.25:
-15/20.25(x^2 + 3x + 2.25)
To simplify this expression further, distribute the -15/20.25:
-15/20.25 * x^2 - 15/20.25 * 3x - 15/20.25 * 2.25
Simplifying the coefficients gives us the final simplified equation:
y = -0.7407x^2 - 0.5556x - 0.3333
2. y = a(x + 2)^2 + 1.5
In this equation, we are given a parameter "a" that we need to determine. However, the FOIL property does not apply here since we only have a binomial squared.
To determine the value of "a," we can use the information given by the quadratic equation. You mentioned that you were looking at two parabolas, which likely means that you have some points from the parabolas.
Let's assume you have a point (x1, y1) on the parabola. Substitute this point into the equation and solve for "a":
y1 = a(x1 + 2)^2 + 1.5
Now, input the known values of y1 and x1 and simplify the equation:
y1 - 1.5 = a(x1 + 2)^2
Solve for "a":
a = (y1 - 1.5) / (x1 + 2)^2
By substituting the coordinates of any known point on the parabola, you can find the corresponding value of "a."