Math Problem Statement
Solution
To write the equation of the parabola in vertex form, we start with the general formula of a parabola in vertex form: where is the vertex of the parabola.
Step 1: Identify the vertex
Given that the vertex is , we have: Thus, the equation becomes:
Step 2: Use the additional point to find
We are given another point that lies on the parabola. Substitute and into the equation to solve for :
Step 3: Write the final equation
Substituting back into the equation, we have:
The equation of the parabola in vertex form is:
Would you like me to explain any part in more detail, or do you have any questions?
Here are 5 related questions to expand your understanding:
- How do you convert a quadratic equation from vertex form to standard form?
- What is the process to find the vertex of a parabola given in standard form?
- How do you determine the direction of a parabola (opening upwards or downwards) from the vertex form?
- How can you find the axis of symmetry from the vertex form equation?
- What does the value of in the vertex form equation tell you about the parabola's width?
Tip:
When the coefficient in the vertex form is negative, the parabola opens downwards; if is positive, it opens upwards.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Vertex Form of a Parabola
Formulas
f(x) = a(x - h)^2 + k
Theorems
Using a point on the parabola to find 'a' in vertex form
Suitable Grade Level
Grades 9-12
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