Question

1. find the equation of the parabola having its vertex at the origin and symmetrical about the x - axis and passing through the point (-4, - 10). sketch its graph.

Explanation:

Step1: Determine the standard - form of the parabola

Since the parabola is symmetric about the x - axis and has its vertex at the origin, its standard form is $y^{2}=4px$ (if it opens to the right or left).

Step2: Substitute the given point into the equation

Substitute the point $(-4,-10)$ into $y^{2}=4px$. We get $(-10)^{2}=4p\times(-4)$.
So, $100 = - 16p$.

Step3: Solve for $p$

Solve the equation $100=-16p$ for $p$. We have $p=-\frac{100}{16}=-\frac{25}{4}$.

Step4: Write the equation of the parabola

Substitute $p =-\frac{25}{4}$ into $y^{2}=4px$. The equation of the parabola is $y^{2}=4\times(-\frac{25}{4})x=-25x$.

Answer:

The equation of the parabola is $y^{2}=-25x$.