# How do you graph y=-3x^2-4x?

Jul 28, 2015

You'll get a parabola.

#### Explanation:

This function is a Quadratic (maximum degree of $x$ is$= 2$) so it will give you a PARABOLA.
Observing the coefficient of ${x}^{2}$ you see that is $- 3$ which is $< 0$ so yours will be a downward parabola.
Now let us try to find interesting points of your parabola that will help us to plot it:

1] y-intercept:
set $x = 0$; you get: $y = 0$

2] x-intercept:
set $y = 0$; you get $- 3 {x}^{2} - 4 x = 0$ solving it you find:
$- x \left(3 x + 4\right) = 0$
so you have two solutions:
${x}_{1} = 0$
${x}_{2} = - \frac{4}{3}$
so the x- intercepts will be:
$x = 0 , y = 0$
$x = - \frac{4}{3} , y = 0$

3] Vertex: this point represents the highest point reached by your parabola. the function can be written as $y = a {x}^{2} + b x + c$
$a = - 3$
$b = - 4$
$c = 0$
The $x$ coordinate of the vertex can then be found considering that $\textcolor{red}{{x}_{v} = - \frac{b}{2 a}} = \frac{4}{- 6} = - \frac{4}{6}$;
The $y$ coordinate of the vertex can then be found considering that $\textcolor{red}{{y}_{v} = - \frac{\Delta}{4 a}} = - \frac{{b}^{2} - 4 a c}{4 a} = \frac{- 16}{- 12} = \frac{4}{3}$