Math Problem Statement
Solution
The given equation represents the path of a projectile, and we are asked to determine its maximum height by finding the vertex of the parabola.
The equation of the parabola is given as:
Step 1: Expand the quadratic expression
First, we expand the product :
So, the equation becomes:
Step 2: Distribute the
Now, the equation is in standard quadratic form:
Step 3: Find the x-coordinate of the vertex
For a quadratic equation , the x-coordinate of the vertex is given by:
Here, and , so:
Step 4: Find the y-coordinate of the vertex
To find the maximum height, we substitute into the equation for :
Substitute :
Thus, the maximum height is:
Conclusion:
The maximum height is approximately units.
Would you like further details or have any questions?
Here are 5 relative questions to explore further:
- How do we derive the vertex formula for a parabola?
- What is the significance of the vertex in projectile motion?
- How does changing the coefficient affect the parabola's shape?
- Can we find the total distance the object traveled horizontally?
- How does the starting point influence the equation?
Tip: In a quadratic equation, the vertex represents the maximum or minimum value, depending on the sign of the leading coefficient .
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Vertex of a Parabola
Projectile Motion
Formulas
Vertex formula for a parabola x = -b/(2a)
Quadratic expansion (x + 1)(17 - x)
Theorems
Vertex Form of a Quadratic Function
Suitable Grade Level
High School
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