This question asks students to substitute or plug in -3 for x so

g(-3) = -2(3)^2 + 3(-3) being careful about order of operations 🙂

Students can check their work by using the TI-84

This question asks students to substitute or plug in -3 for x so

g(-3) = -2(3)^2 + 3(-3) being careful about order of operations 🙂

Students can check their work by using the TI-84

The left hand side of the equation is almost a perfect square:

In order for it to be a perfect square: x^2 + 4x + ____ = 2 + ____

To find the number that completes the square take 1/2 of 4 and square it

So 4 gets added to both sides

Then the right side becomes 6

Then we can write the left side like this: (x + 2) ^2

So (x + 2)^2 = 6

then take the sqrt of both sides but do not forget the +/- with the sqrt

Then subtract 2 from both sides:

You will have two answers a plus and a minus and you can check your work by using the quadratic formula 🙂

To solve a quadratic equation ax^2 + bx + c = 0, wecan use the quadratic formula above given on the Regents Reference Sheet.

In order to find out if a solution is rational or irrational, we focus on the algebra under the radical: b^2 – 4ac: If b^2 – 4ac is a perfect square, then when we take the square root, we will get a rational number but if b^2 – 4ac is not a perfect square (like 4, 9, 16 etc), then the solution will be irrational.

In the equation 2x^2 + 3x – 10 =0, a=2, b=3 and c = -10

Once you substitute in those numbers into b^2 – 4ac, do you get a perfect square or not?

Average rate of change is another name for slope

(big hint given in the units feet per second).

Slope is change in y / change in x — the slope formula is (y2 – y1)/(x2 – x1)

Use the two points (3, 6.26) and (9, 3.41) for (x1, y1) and (x2,y2).

Show your work. Because 3.41 is less than 6.26, your answer should be negative.

For this question, use the TI-84 to find the x values that make y=0. Use the table and then check your answers on the graph. Show and explain all your work.