Concept explainers
Draw the graph .Find the vertex , axis of symmetry and all the intercepts.
Answer to Problem 11WE
Vertex :
Axis of Symmetry : x = -1
y -intercept : (0,-7.5)
x -intercepts are (-5,0) and (3,0)
Explanation of Solution
Given Information:
Given equation is :
Concept Used :
- Parent Function:
- Vertex = (0,0)
- Type of Graph:
- Axis of Symmetry: Passes through the vertex and divides the parabola into two congruent halves.
Upward Parabola
- y -intercept = The y coordinate of the point at which the graph intersects y -axis , x = 0.
- x -intercept = The x coordinate of the point at which the graph intersects x -axis , y = 0 .
Calculation:
- Find Axis of Symmetry :
The equation of axis of symmetry is x = -1
- Find y -intercept :
The y -coordinate of the point at which the graph cuts the y -axis is the y -intercept.
Hence , substituting x =0 in the equation
So, y -intercept = (0,-7.5)
- Find x -intercept :
The x -coordinate of the point at which the graph cuts the x -axis is the x -intercept.
Hence , substituting y =0 in the equation
So, x -intercepts are (3,0) and (-5,0).
Use the above information to graph the equation
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Algebra and Trigonometry: Structure and Method, Book 2
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