Characteristics of Parabolas

Explore the key characteristics of parabolas including vertex, axis of symmetry, intercepts, and direction of opening.

Grade 9 Math AlgebraCharacteristics of Parabolas

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Includes

Multiple ChoiceFill in the BlanksShort AnswerCustomTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7.ACCSS.MATH.CONTENT.HSF.BF.B.3

Topics

MathAlgebraParabolasQuadratic FunctionsGrade 9

7 sections · Free to use · Printable

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. What is the name of the highest or lowest point on a parabola?

Focus

Vertex

Directrix

Axis of symmetry

2. If the leading coefficient (a) of a quadratic equation is negative, in which direction does the parabola open?

Upwards

Downwards

Left

Right

3. The vertical line that passes through the vertex of a parabola and divides it into two symmetrical halves is called the .

4. The x-intercepts of a parabola are also known as the or of the quadratic function.

5. For the quadratic function y = x² - 4x + 3, find the coordinates of the vertex and the equation of the axis of symmetry.

6. Determine the x-intercepts and y-intercept for the parabola defined by the equation y = x² + 2x - 8.

7. For the parabola y = -x² + 6x - 5:

a) Find the vertex.

b) Find the axis of symmetry.

c) Find the y-intercept.

d) Find the x-intercepts.

e) Sketch the parabola on the graph below, labeling the vertex and intercepts.

8. A parabola can have three x-intercepts.

True

False

9. The discriminant of a quadratic equation (b² - 4ac) can tell you the number of x-intercepts a parabola has.

True

False