What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)?

x=6

x=2

Step-by-step explanation:

Fortunately for us, the function is written in factorized terms, so it is easier to find its roots.

The roots are the values for the 'x' variables that makes the functions goes to zero.

They are x=6 and x=2, any of those value make the function equals zero, or in other words, they are the points of interception with the 'y' axis.

To obtain these value

lets study the following condition

(x-6) * (x-2)=0

The above is accomplish when (x-6)=0 or (x-2)=0

We have two independent equations from where we obtain that x=6 and x=2

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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