Factor this expression completely. X^2-2x+24
2 answers:
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The equation of the parabola is y = 0.015x^2 + 0.06x + 1
<h3>The linear equations</h3>A parabola is represented as:
y = ax^2 + bx + c
The points are given as:
(-4,1), (-2,0.94) and (0,1)
When these points are substituted in y = ax^2 + bx + c, we have the following linear equations
16a - 4b + c = 1
4a - 2b + c = 0.94
c = 1
<h3>The matrix that represent the system of equations</h3>In (a), we have:
16a - 4b + c = 1
4a - 2b + c = 0.94
c = 1
Remove the variables (leaving the coefficients)
a b c
16 -4 1 1
4 -2 1 0.94
0 0 1 1
So, the matrix representation of the system of equations is:
Using a graphing calculator, we have the inverse of the coefficient matrix to be
Using a graphing calculator, we have the solution to the system of equations to be
a = 0.015
b = 0.06
c = 1
Recall that:
y = ax^2 + bx + c
So, we have:
y = 0.015x^2 + 0.06x + 1
Hence, the equation of the parabola is y = 0.015x^2 + 0.06x + 1
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