### Posts Tagged ‘precalc11’

This week we learned how to graph inequalities with two variables. These inequalities are essentially forms of the equation y=mx+b, used to graph lines. The same idea can be applied to graphing the inequalities.

However depending on the inequality the line will either be broken or solid.

solid line = $\leq$ or $\geq$

broken line = $>$ or $<$

using the same idea as y=mx+b, we can find the slope, and the y-intercept.

“m” represents our slope, if it’s a whole number it can be read as $\frac{n}{1}$ with “n” being your rise(y), and 1 being your run(x).

For instance: If you were to graph $y>x+2$, your y-intercept would be 2, and your slope would be $\frac{1}{1}$

It would look like this: The area shaded, is figured out by testing x and y coordinates in your equation, until the equation is made true through the coordinates chosen.

This week we learned about graphing quadratic equations in factored form. In factored form, we can find the roots, as well as the axis of symmetry. With this information, we can draw a quick graph depicting what our parabola would look like.

ex. Graph the equation $y=-2x^2-6x+20$

graphing the equation with only the factored form won’t give us a complete parabola, but it will give us enough information to get a rough idea. $y=-2(x^2+3x-10$

\$latex y=-2(x+5)(x-2)

replace the “y” with 0.

0=-2(x+5)(x-2)

rearranging the bracketed “x’s” will give us our roots

(x+5) -> x=-5, (x-2) -> x=2

with the x-intercepts, we know that when graphed will be in the format (x,y). But since the x-intercept is where the parabola crosses the x-axis, the y-intercept will equal 0. The x-intercepts will be (-5,0) and (2,0). The axis of symmetry is half way between both roots, so the AOS will be x=-1.5.