Find Point C on f(x)=x²-8x+16: Quadratic Function Graph Analysis

Question

The following function has been plotted on the graph below:

$f(x)=x^2-8x+16$

Calculate point C.

00:00 Find the coordinates of point C

00:06 At point C Y=0, the point is on the X-axis

00:10 Substitute Y=0 in the function and solve for X

00:19 We want to factor the function into a trinomial

00:23 This is the appropriate factorization

00:30 Isolate X

00:35 And this is the solution to the question

To solve the exercise, first note that point C lies on the X-axis.

Therefore, to find it, we need to understand what is the X value when Y equals 0.

Let's set the equation equal to 0:

0=x²-8x+16

We'll use the preferred method (trinomial or quadratic formula) to find the X values, and we'll discover that

X=4

$(4,0)$