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Chapter 6: Problem 30

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Vertical axis and passes through the point (-3,-3)

Short Answer

Expert verified
The standard form of the equation of the parabola is \(y = -1/3*x^2\).

Step by step solution

01

Write down the standard form of the equation

The standard form of the equation of a parabola with a vertex at the origin and a vertical axis is \(y = ax^2\). We now need to determine the value of 'a'.
02

Substitute the given point into the equation

The given point is (-3, -3). We substitute these values for 'x' and 'y' into the standard form equation to get \(-3 = a*(-3)^2\).
03

Solve for 'a'

Solving the equation in step 2 for 'a', we get \(a = -3/9 = -1/3\). Therefore, 'a' is -1/3.
04

Write the final equation of the parabola

Substituting 'a' back to the standard form of the equation, we get the equation of the parabola as \(y = -1/3*x^2\).

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