Honors Algebra 2: Semester 1 Final Exam Review

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What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or zero) of a polynomial equation, in the form of p/q, is such that p is a factor of the constant term and q is a factor of the leading coefficient.

Front

How do you find the starting height of a projectile given its height equation?

Back

To find the starting height of a projectile, evaluate the height equation at t=0. For example, in h(t) = -16t² + 140t + 2, h(0) = 2 feet.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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How do you determine the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the equation equal to zero and solve for x using factoring, the quadratic formula, or completing the square.

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What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

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What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It represents the maximum or minimum value of the function.

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What is the difference between consistent and inconsistent systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

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How do you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.

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What are the characteristics of a parabola?

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A parabola opens upwards or downwards, has a vertex, an axis of symmetry, and can be described by its width and direction of opening.