Analyzing f(x) Using Precalculus

  • Thread starter Thread starter rocomath
  • Start date Start date
  • Tags Tags
    Precalculus
AI Thread Summary
The discussion focuses on analyzing the quadratic function f(x) = -4x^2 + 4x by converting it into vertex form. The transformation involves completing the square, resulting in f(x) = -4(x - 1/2)^2 + 1. This form highlights the vertex of the parabola at the point (1/2, 1) and indicates that the parabola opens downward due to the negative leading coefficient. The process demonstrates the application of precalculus techniques to analyze the properties of quadratic functions. Understanding this transformation is essential for graphing and interpreting the behavior of the function.
rocomath
Messages
1,752
Reaction score
1
Precal

f(x)=-4x^2+4x \rightarrow f(x)=a(x-h)^2+k

f(x)=-4(x^2-x)

f(x)=-4\left[x^2-x+\left(\frac 1 2\right)^2-\left(\frac 1 2\right)^2\right]

f(x)=-4\left[x^2-x+\left(\frac 1 2\right)^2-\frac 1 4\right]

f(x)=-4\left[x^2-x+\left(\frac 1 2\right)^2\right]+1

f(x)=-4\left(x-\frac 1 2\right)^2+1
 
Last edited:
Physics news on Phys.org
Good
 
Back
Top