Math Problem Statement
Solution
The quadratic function provided is:
To find the y-value of the vertex of this quadratic, we can follow these steps:
1. Find the x-coordinate of the vertex:
The x-coordinate of the vertex for a quadratic equation can be found using the formula:
In this case, and . Plugging these values into the formula:
2. Find the y-value (f(x)) at the vertex:
Now substitute into the function to find the y-value:
Let's compute this step-by-step:
Simplify further:
Thus, the y-value of the vertex is:
Would you like more details or have any questions?
Here are 5 related questions:
- How do you find the vertex of a quadratic equation in vertex form?
- What does the vertex of a parabola represent in real-world contexts?
- How do you determine whether the vertex is a maximum or minimum?
- Can the quadratic formula be used to find the vertex?
- How does changing the coefficient of affect the shape of the parabola?
Tip: For any quadratic equation, the vertex formula is a quick way to find the turning point of the parabola.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Vertex of a Parabola
Formulas
x = -b / 2a
y = f(x) for the vertex
Theorems
Vertex Formula for a Quadratic Equation
Suitable Grade Level
Grades 8-10