Problem 98
Question
Write the equation of each parabola in standard form. Vertex: \((-3,-1) ;\) The graph passes through the point \((-2,-3)\)
Step-by-Step Solution
Verified Answer
The equation of the parabola in standard form is \(y = -2(x + 3)^2 - 1\)
1Step 1: Insert Vertex into General Equation
Insert the provided vertex coordinates \((-3, -1)\) into the general equation to get \(y + 1 = a(x + 3)^2\)
2Step 2: 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.\
3Step 3: Solve for 'a'
After substitution, we can simplify to get: \(-2 = a(1)^2\). Solving for 'a' will result in \(a = -2.\)
4Step 4: 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 \(y = -2(x + 3)^2 - 1\).
Other exercises in this chapter
Problem 98
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