1. Find the vertex of the following quadratic equations:
a) f(x) = (x – 4)2 + 7

It is not possible to find the vertex of the stated equation as it is in the form of f(x) = mx + b, a linear equation.

Step-by-step explanation:

Being in the form f(x) = mx + b, it is not possible to find a vertex due to the fact that there is none. This is because when an equation is written in the linear form it is representing a line not a parabola.

Given a parabola it is possible to find a vertex because in that case there is one.

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus