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Questions and Answers
What information about a parabola can be determined from its vertex?
What information about a parabola can be determined from its vertex?
The vertex gives the maximum or minimum point of the parabola and indicates whether it opens upward or downward.
How do you determine the x-intercepts of a quadratic function?
How do you determine the x-intercepts of a quadratic function?
The x-intercepts can be found by setting the quadratic equation to zero and solving for x.
What does the axis of symmetry of a parabola represent?
What does the axis of symmetry of a parabola represent?
The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.
What is the standard form of a quadratic function?
What is the standard form of a quadratic function?
Describe how to find the maximum or minimum value of a quadratic function.
Describe how to find the maximum or minimum value of a quadratic function.
How does the leading coefficient of a quadratic function affect the graph?
How does the leading coefficient of a quadratic function affect the graph?
What role does the discriminant play in finding the roots of a quadratic equation?
What role does the discriminant play in finding the roots of a quadratic equation?
How do you convert a quadratic function from vertex form to standard form?
How do you convert a quadratic function from vertex form to standard form?
List the multiplicities of the zeros for the polynomial function $f(x) = 6x(x-13)(x+2)^3$.
List the multiplicities of the zeros for the polynomial function $f(x) = 6x(x-13)(x+2)^3$.
What is the factored form of a fourth-degree polynomial having zeros at -4, 2, 3, and -5?
What is the factored form of a fourth-degree polynomial having zeros at -4, 2, 3, and -5?
Identify the $y$-intercept and all $x$-intercepts of the function $f(x) = 2x^3 + 2x^2 - 24x$.
Identify the $y$-intercept and all $x$-intercepts of the function $f(x) = 2x^3 + 2x^2 - 24x$.
Describe the end behavior of the polynomial function $f(x) = 6x^6 - 3x^4 - 4x^3 + 6x^2$.
Describe the end behavior of the polynomial function $f(x) = 6x^6 - 3x^4 - 4x^3 + 6x^2$.
For the inequality $(x+4)(x-7) ≥ 0$, what is the correct solution set?
For the inequality $(x+4)(x-7) ≥ 0$, what is the correct solution set?
What are the results of the division $(6x^3 + 9x^2 + 21x + 11) ÷ (3x^2 + 3x)$?
What are the results of the division $(6x^3 + 9x^2 + 21x + 11) ÷ (3x^2 + 3x)$?
What is the quotient and remainder when using synthetic division on $-4x^3 + 12x^2 + 18x - 14x + 24$ divided by $x - 4$?
What is the quotient and remainder when using synthetic division on $-4x^3 + 12x^2 + 18x - 14x + 24$ divided by $x - 4$?
What is the leading coefficient of the polynomial $-10 + 18x^6 + 4x^3$ and what is its degree?
What is the leading coefficient of the polynomial $-10 + 18x^6 + 4x^3$ and what is its degree?
What intervals identify where the function increases based on its local extrema?
What intervals identify where the function increases based on its local extrema?
Simplify the expression $ rac{6x^2 + 11x}{2x}$ and provide the result.
Simplify the expression $ rac{6x^2 + 11x}{2x}$ and provide the result.
From the polynomial function $f(x) = -5x^3 + 4x^2 - 8x - 1$, what is its end behavior?
From the polynomial function $f(x) = -5x^3 + 4x^2 - 8x - 1$, what is its end behavior?
Using the remainder theorem, what is the value of $P(2)$ for the polynomial $P(x) = x^3 - 2x^2 - 4$?
Using the remainder theorem, what is the value of $P(2)$ for the polynomial $P(x) = x^3 - 2x^2 - 4$?
Identify the signs of the leading coefficient and suggest a possible degree for the function with positive leading coefficient.
Identify the signs of the leading coefficient and suggest a possible degree for the function with positive leading coefficient.
For the quadratic $y = -3x^2$, which direction does the parabola open?
For the quadratic $y = -3x^2$, which direction does the parabola open?
Find the real zeros of the function $f(x) = -5x(x^2 - 16)(x^2 + 36)$.
Find the real zeros of the function $f(x) = -5x(x^2 - 16)(x^2 + 36)$.
In the polynomial function $f(x) = 4x(x-4)(x+2)$, what is the end behavior?
In the polynomial function $f(x) = 4x(x-4)(x+2)$, what is the end behavior?
Study Notes
Rational Zeros Theorem
- The Rational Zeros Theorem states that all possible rational zeros of a polynomial can be found by dividing the factors of the constant term by the factors of the leading coefficient.
- For the polynomial, the constant term is -3 and the leading coefficient is 2.
- The factors of -3 are ± 1 and ± 3.
- The factors of 2 are ± 1 and ± 2.
- Therefore, the possible rational zeros are: ± 1/2, ± 1, ± 3/2, ± 3.
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Description
Test your knowledge of the Rational Zeros Theorem with this quiz! Dive into the concept of finding all possible rational zeros of a polynomial using the factors of the constant term and leading coefficient. Challenge yourself with various problems and applications!
