Suggested languages for you:

Americas

Europe

Problem 752

# Find the equation of a parabola that has vertex at $$(-1,2)$$, axis of symmetry parallel to the $$\mathrm{x}$$ -axis, and goes through the point $$\mathrm{P}_{1}(-3,-4)$$.

Expert verified
The equation of the parabola is $$y = -\frac{3}{2}(x+1)^2 +2$$.
See the step by step solution

## Step 1: Write the vertex form of the parabola equation using the given vertex coordinates.

We are given the vertex coordinates (-1, 2). So, the vertex form of the parabola equation will be: $$y = a(x-(-1))^2+2$$ Simplify the equation: $$y = a(x+1)^2 +2$$

## Step 2: Use the point P1 to find the value of 'a'.

We know the parabola goes through the point P1(-3, -4). We can substitute these coordinates into the equation we found in Step 1 and solve for "a": $$-4 = a(-3+1)^2 +2$$

## Step 3: Solve for 'a'.

Simplify the equation and solve for "a": $$-4 = a(-2)^2 +2$$ $$-4 = 4a +2$$ Subtract 2 from both sides: $$-6 = 4a$$ Now, divide by 4: $$a = -\frac{3}{2}$$

## Step 4: Write the equation of the parabola.

Now that we have the value of "a", we can write the final equation of the parabola: $$y = -\frac{3}{2}(x+1)^2 +2$$ This is the equation of the parabola with vertex at (-1, 2), axis of symmetry parallel to the x-axis, and going through the point P1(-3, -4).

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features

## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner