Analyzing f(x) Using Precalculus

[rocomath]

Precal

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

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

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

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

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

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

 

[symbolipoint]

Good

 

[Architeuthis Dux]

This is an example of completing the square to rewrite a quadratic function in vertex form, where a is the coefficient of the squared term, h and k are the coordinates of the vertex, and the value of k represents the y-intercept. By analyzing the given function using precalculus concepts, we were able to manipulate it into a form that provides valuable information about the function, such as the vertex and y-intercept. This can be useful in graphing the function and understanding its behavior. Precalculus allows us to use algebraic techniques to analyze and manipulate functions, providing a deeper understanding of their properties.