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Chapter 3: Problem 98

Write the equation of each parabola in standard form. Vertex: \((-3,-1) ;\) The graph passes through the point \((-2,-3)\)

Short Answer

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

Step by step solution

01

Insert Vertex into General Equation

Insert the provided vertex coordinates \((-3, -1)\) into the general equation to get \(y + 1 = a(x + 3)^2\)
02

Substitute the coordinates of the given point into the equation

Given that the graph passes through the point \((-2, -3)\), we can substitute these coordinates into the equation. Hence, we would get: \(-3 + 1 = a(-2 + 3)^2.\
03

Solve for 'a'

After substitution, we can simplify to get: \(-2 = a(1)^2\). Solving for 'a' will result in \(a = -2.\)
04

Write the equation in standard form using the found 'a'

We substitute 'a' into the equation obtained in step 1 to get the equation of the parabola in standard form: \(y + 1 = -2(x + 3)^2\), which can be rewritten as \(y = -2(x + 3)^2 - 1\).

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