What is the solution set for the given equation? 3|x + 4| = 18

Let's try a different approach this time...

3|x + 4| = 18

has the same solution as

|x + 4| = 6


We look for the number(s) that can add/subtract to obtain 6. We can see that x=2 will work. No other positive number will work, however if we consider negative numbers then -10 seems possible. In fact is does work because |-10+4| = |-6| = 6. So x=-10.

What is the number of turning points in the graph of the function of x defined below?

y = 2x² + 5x - 7

Solution:

The polynomial y has degree n=2 so the maximum number of turns it can have is n-1 = 2-1 = 1. (In fact we know that our polynomial is a quadratic and it opens upwards so this is another way to know it only has one turn).

Find x.

What is the value of x?

Solution:


TV is a diameter, and SU is perpendicular to TV. This means that x=8

The polynomial equation x(x2+4)(x2-x-6)=0 has how many real roots?

Solution:

x2+4 contributes complex zeros. This means that the factors x and x2-x-6 contribute real zeros. Therefore the polynomial has 3 real zeros

What are the coordinates of the vertex of the graph of the function -2(x - 1)2 = y + 5?

so the vertex is (1,5)

If f(x) = 5x2 - 7, what is f(-3)?

Given quadrilateral KLMN, what is the value of x?

Given quadrilateral KLMN, what is the value of x?


Solution:

3x+x+25+80+95=360 (why?)

4x+200=360

4x=160

x=40