Math Problem Statement
Find the x- and y-intercepts from the graph of the equation y = 3x - x^2.
Solution
From the graph and the equation , let's determine the intercepts.
Finding the x-intercepts:
The x-intercepts occur where . Setting the equation to zero: Factoring out : Setting each factor equal to zero:
Finding the y-intercept:
The y-intercept occurs where . Substituting into the equation:
Solutions:
- x-intercept (smaller x-value):
- x-intercept (larger x-value):
- y-intercept:
These answers are consistent with the graph provided. If you have any questions or need further details, feel free to ask.
Related Questions:
- How do you determine the vertex of the parabola ?
- What is the axis of symmetry for the equation ?
- How can you verify the intercepts algebraically without a graph?
- What transformations have been applied if the original equation was ?
- How would the graph change if the equation was ?
Tip:
When you have a quadratic equation in the form , setting and factoring can directly give you the x-intercepts.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Intercepts
Factoring
Formulas
Quadratic equation: y = ax^2 + bx + c
Intercepts: Solve for x when y = 0 (for x-intercepts), solve for y when x = 0 (for y-intercept)
Theorems
Factoring method to solve quadratic equations
Suitable Grade Level
Grades 8-10