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Concept explainers
a.
To graph the given equation.
a.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given information :
Given function is
Graph :
Interpretation :
The graph of a
This vertex point shall be:
Highest point (if
Or, lowest point (if
In this case, ‘a’ is lesser than 0 hence the graph will have a maximum and will open downwards.
A parabola always points to infinity, either negative or positive.
To graph a quadratic function, compute the axis of symmetry, vertex and y-intercept, post which, plot the same on a graph.
The axis of symmetry bisects the parabola into two equal parts. Hence each point on the parabola would have an equal point on the other side of the axis of symmetry. Plot these points on the graph with a smooth curve.
Formula to compute equation of the axis of symmetry
Axis of symmetry for the given function is
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
Simplifying this
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y . These two coordinates of x and y would be the point where the vertex is.
Putting the value of
Simplifying the expression.
Thus the vertex is
y-intercept is computed by substituting the value of x in the equation by 0.
Simplifying
Hence the point of y-intercept is
Now, plot these points along with their reflecting symmetric points, starting from the vertex.
b.
To calculate the height from which the ball is thrown.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 21CYU
The height from with the ball is thrown is 5 feet .
Explanation of Solution
Given information :
The function provided is
Formula used :
The ball is thrown from a certain height. This can be calculated by finding the y-intercept of the equation.
For finding the y-intercept, substitute the value of x in the function with 0 and compute the value of y . Y -intercept is always given by the notion (0,y) .
Calculation :
y-intercept is computed by substituting the value of x in the equation by 0.
Simplifying
Hence the point of y-intercept is
Thus it can be said that the ball was initially at the height of 5 feet . This is the y coordinate of the point of the y-intercept.
c.
To calculate the maximum height that the ball reaches.
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 21CYU
The maximum height that the ball reaches is 9 feet .
Explanation of Solution
Given information :
The function provided is
Formula used :
The maximum height can be calculated using the vertex formula. Here, find the y-coordinate of the point of the vertex. This value will be the maximum height attained by the ball.
Calculation :
Time at which the ball reaches maximum height.
Putting the values of ‘a’ and ‘b’ .
Simplifying
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y , that will be the maximum height in feet.
Putting the value of
Simplifying the expression.
Thus, the maximum height is at 9 feet .
Chapter 9 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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