Math Problem Statement
Find the intercepts and graph the equation by plotting points. yequalsx squared minus 4 Question content area bottom left Part 1 What are the intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are enter your response here. (Use a comma to separate answers as needed. Type an ordered pair.)
Solution
To find the intercepts of the equation , we need to determine where the graph crosses the x-axis and the y-axis.
X-intercepts:
X-intercepts occur where . So, set and solve for :
This simplifies to:
Taking the square root of both sides:
Thus, the x-intercepts are at and .
Y-intercept:
The y-intercept occurs where . Plug into the equation:
Thus, the y-intercept is at .
Intercepts:
- X-intercepts: and
- Y-intercept:
Would you like to see the graph, or do you have any questions about the solution?
Here are 5 questions to expand your understanding:
- How would the graph change if the equation was ?
- What would the intercepts be if the equation was ?
- What is the vertex of the parabola represented by ?
- How do the intercepts relate to the symmetry of the parabola?
- Can you find the axis of symmetry for the parabola?
Tip: When solving for x-intercepts, always remember to set and solve for .
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Graphing
Formulas
Standard form of a quadratic equation: y = ax^2 + bx + c
Finding intercepts: Set y = 0 for x-intercepts and x = 0 for y-intercepts
Theorems
Properties of quadratic functions
Symmetry of parabolas
Suitable Grade Level
Grades 8-10