Math Problem Statement
Graph the equation. Select integers for x from -3 to 3, inclusive. y = x^2 - 4
Solution
The given equation is , and you are asked to graph it for integer values of from to , inclusive.
Let's first compute the corresponding -values for each -value in that range:
- For :
- For :
- For :
- For :
- For :
- For :
- For :
Now that we have the points , , , , , , and , we can plot these on a graph. The shape of the graph will be a parabola, as this is a quadratic equation.
Would you like me to provide the graph as well?
Expanding the concept:
- What is the general shape of a quadratic function like ?
- How would the graph change if the equation were ?
- What is the vertex of the parabola for the equation ?
- How does the value of in affect the graph's position?
- What happens to the graph if we change the equation to ?
Tip:
In a quadratic function , the coefficient controls the direction and width of the parabola, while controls the vertical shift.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Graphing
Formulas
Quadratic equation in the form y = ax^2 + bx + c
Theorems
Properties of quadratic functions
Graph of a parabola
Suitable Grade Level
Grades 8-10