Effect of the Real Numbers h and k of a

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Presentation transcript:

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. 1 of 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. 2 of 2

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. 1 of 2

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. 2 of 2

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.