Exam 6: Factoring and Quadratic Equations

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Find the vertex of the given equation and determine whether it is a maximum or minimum point. Find the vertex of the given equation and determine whether it is a maximum or minimum point.

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C

For the polynomial expression factor out the GCF. For the polynomial expression factor out the GCF.

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C

Solve the equation by factoring. Solve the equation by factoring.

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A

Factor the trinomial. If the trinomial cannot be factored over the integers then write that it is prime. Factor the trinomial. If the trinomial cannot be factored over the integers then write that it is prime.

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Factor the polynomial expression. If the polynomial cannot be factored write the answer as prime. Factor the polynomial expression. If the polynomial cannot be factored write the answer as prime.

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Match the equation with its graph.
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Graph the equation using symmetry. Label the vertex and the x- and y-intercepts. Graph the equation using symmetry. Label the vertex and the x- and y-intercepts.    Graph the equation using symmetry. Label the vertex and the x- and y-intercepts.

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Factor the polynomial expression completely. If the polynomial cannot be factored write the answer as prime. Factor the polynomial expression completely. If the polynomial cannot be factored write the answer as prime.

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A polynomial that cannot be factored over the set of integers is called prime.

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The graphs of The graphs of   and   are given below. Which one of the following is the graph of   ?  and The graphs of   and   are given below. Which one of the following is the graph of   ?  are given below. Which one of the following is the graph of The graphs of   and   are given below. Which one of the following is the graph of   ?  ? The graphs of   and   are given below. Which one of the following is the graph of   ?

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For the polynomial expression factor out the GCF. For the polynomial expression factor out the GCF.

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Graph the equation using symmetry. Label the vertex and the x- and y-intercepts. Graph the equation using symmetry. Label the vertex and the x- and y-intercepts.    Graph the equation using symmetry. Label the vertex and the x- and y-intercepts.

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Find the axis of symmetry for the given equation. Find the axis of symmetry for the given equation.

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Factor the polynomial expression by grouping. Factor the polynomial expression by grouping.

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Which one of the following is the equation of the horizontal asymptote for Which one of the following is the equation of the horizontal asymptote for   ? ?

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Match the appropriate word to complete each sentence.
If the leading coefficient a in a quadratic equation in two variables is a negative number the graph of the equation opens __________.
up
If the leading coefficient a in a quadratic equation in two variables is a positive number the graph of the equation opens __________.
parabola
The vertical line that goes through the vertex of a parabola is the __________.
vertex
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If the leading coefficient a in a quadratic equation in two variables is a negative number the graph of the equation opens __________.
up
If the leading coefficient a in a quadratic equation in two variables is a positive number the graph of the equation opens __________.
parabola
The vertical line that goes through the vertex of a parabola is the __________.
vertex
The __________ of a parabola is the lowest point for a parabola that opens upward and it is the highest point for a parabola that opens downward.
axis of symmetry
The graph of a quadratic equation in two variables is a __________.
down
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Use the table below to find Use the table below to find

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The profit per item in your factory making widgets can be approximated by the equation The profit per item in your factory making widgets can be approximated by the equation   when you make n widgets. How many widgets must be made for the profit per item to be $215? when you make n widgets. How many widgets must be made for the profit per item to be $215?

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Factor the trinomial. If the trinomial cannot be factored over the integers then write that it is prime. Factor the trinomial. If the trinomial cannot be factored over the integers then write that it is prime.

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The zero-product property states that if any two numbers are multiplied together to get zero then one or both of the two numbers must be zero. We use this property to solve some quadratic equations. This means that the number zero (0) is always a solution to each of these equations.

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