Math Problem Statement

The height, in feet, of a ball thrown by a child is y= -12x2+2x+4 , where x is the horizontal distance, in feet, from where the ball was thrown.

How high was the ball when it left the child’s hand?

How high was the ball when it was at its maximum height?

How far from the child did the ball strike the ground?

Solution

The equation of the height yy of the ball is given by:

y=−12x2+2x+4y = -12x^2 + 2x + 4

where xx represents the horizontal distance from where the ball was thrown. Let's answer each question in turn.

1. How high was the ball when it left the child’s hand?

The height of the ball when it left the child's hand corresponds to x=0x = 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Vertex of a Parabola
Roots of Equations

Formulas

Quadratic equation formula: ax^2 + bx + c = 0
Vertex formula: x = -b / (2a)
Root-finding using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Theorems

Quadratic formula
Properties of Parabolas

Suitable Grade Level

Grades 8-10

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