Math Problem Statement
vertex form when vertex is (-1/4, 3/2) and a point is (-2,0)
Solution
To find the vertex form of a quadratic equation, we use the following formula:
where is the vertex of the parabola, and is a constant that determines how wide or narrow the parabola is.
Given:
- Vertex:
- A point on the parabola:
Step 1: Plug in the vertex into the vertex form.
Now, we need to find the value of using the point .
Step 2: Substitute the point into the equation.
Simplify inside the parentheses: So:
Step 3: Simplify the equation.
Step 4: Solve for .
First, subtract from both sides:
Now, multiply both sides by to isolate :
Step 5: Write the final equation.
Now that we know , the vertex form of the equation is:
Do you need further details or clarification?
Here are five related questions:
- How do you convert vertex form to standard form?
- How do you determine the direction of a parabola using ?
- What does the vertex of a quadratic function represent?
- How can you find the x-intercepts from vertex form?
- How do you complete the square to transform a standard form equation into vertex form?
Tip: The sign of determines whether the parabola opens upwards () or downwards ().
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex Form of a Parabola
Formulas
y = a(x - h)^2 + k (Vertex Form of a Quadratic Equation)
Theorems
Quadratic Functions Theorem (relating the vertex form to the standard form)
Suitable Grade Level
Grades 10-12
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