`y = x^2 - 6x + 5` Write the quadratic in intercept form and give the function's zeros.
The intercept form is: y = a (x - p) (x - q)
In the given equation y = x^2 - 6x + 5, you can find the x-intercepts.
make y 0, then factor the equation to get:
0 = (x - 5) (x - 1)
so the x intercepts are 5 and 1.
Now, plug in the x- intercepts for p and q.
y = a (x - 1) (x - 5)
Find a by randomly picking a point from the graph and plugging it in. To consume time, you can find the y-intercepts so you have both the 0's for x and y, then plug the y-intercept into the equation.
Find the y-intercept by making x 0 in the original factorised equation.
y = (0 - 5) (0 - 1)
= y = (-5) (-1)
= y = 5
so the y-intercept is 5.
Now, using this point (0,5), plug it into the half-complete intercept form.
5 = a (0 - 1) (0 - 5)
You can tell that this is the same as when trying to solve for the y-intercept, so we can tell that a is 1. So, the final intercept form equation would be:
y = (x - 1) (x - 5)