1. Effect of the Real Numbers h and k of a
Chapter 12
Discovery 1
Effect of the Real Numbers h and k of a
Quadratic Equation on a Parabola
1. Sketch the graphs of the following quadratic equations of the form
where a = 1 and h = 0. Label the vertex of each graph.
2. Write a rule for determining the y-coordinate of the vertex of a parabola from the
equation of the parabola.
3. Sketch the graphs of the following quadratic equations of the form
where a = 1 and k = 0. Label the vertex of each graph.
4. Write a rule for determining the x-coordinate of the vertex of a parabola from the
equation of the parabola.
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2. Effect of the Real Numbers h and k of a
Chapter 12
Discovery 1
Effect of the Real Numbers h and k of a
Quadratic Equation on a Parabola
5. Sketch the graphs of the following quadratic equations of the form
where a = 1. Label the vertex of each graph.
6. Write a rule for determining the coordinates of the vertex of a
parabola from the equation of the parabola.
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3. Effect of the Real Numbers a and b on the Shape of an Ellipse
Chapter 12
Discovery 2
Effect of the Real Numbers a and b
on the Shape of an Ellipse
1. Sketch the graphs of the following equations in the form ,
where a > b:
Label the x- and y-intercepts.
2. Sketch the graphs of the following equations in the form ,
where a < b:
Label the x- and y-intercepts.
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4. Effect of the Real Numbers a and b on the Shape of an Ellipse
Chapter 12
Discovery 2
Effect of the Real Numbers a and b
on the Shape of an Ellipse
3. Sketch the graphs of the following equations in the form ,
where a = b:
Label the x- and y-intercepts.
Write a rule for determining the shape of an ellipse from its equation.
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5. Effect of the Form of the Equation on the Orientation of the Hyperbola
Chapter 12
Discovery 3
Effect of the Form of the Equation
on the Orientation of the Hyperbola
1. Sketch the graphs of the following equations in the form :
2. Sketch the graphs of the following equations in the form :
Write a rule for explaining the orientation of a hyperbola from its
equation.