Question

challenge #6
plot five parabolas, one through each set of color points.
when you finish, press \check my work\.
parabola equation
red
blue
green
orange
purple
check my work

Explanation:

Step1: Recall the general form of a parabola

The general form of a parabola is $y = ax^{2}+bx + c$.

Step2: Use given points to find coefficients

For example, if a parabola passes through $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$, we substitute these points into $y = ax^{2}+bx + c$ to get a system of linear - equations:

$$
LATEXBLOCK0
$$

Solve the system to find $a$, $b$ and $c$.

Step3: Plot the parabola

Once we have the equation of the parabola $y = ax^{2}+bx + c$, we can find several points on the parabola by choosing different $x$ - values, calculating the corresponding $y$ - values, and then plot these points on the coordinate plane and connect them with a smooth curve.

Since the specific sets of points for each color are not fully visible, we can't provide the exact equations and plots. But the general process is as above.

Answer:

The process to plot the parabolas is to first find their equations using the points they pass through and then plot points based on the equations.