Mid-term algebra 2 /2025

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What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

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How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form f(x) = ax² + bx + c to vertex form, complete the square.

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What is the solution to the equation |2x - 3| + 5 = 10?

Back

The solutions are x = -1 and x = 4.

Front

What are the roots of the polynomial y = x³ - 3x² - x + 3?

Back

The roots are x = -1, x = 1, and x = 3.

Front

How do you factor the expression x² + 9x - 36?

Back

The expression factors to (x + 12)(x - 3).

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Back

The result is 4x² + 3x - 5.

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What is the quadratic formula used for?

Back

The quadratic formula is used to find the roots of a quadratic equation ax² + bx + c = 0, given by x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

What does it mean for a function to be in vertex form?

Back

A function is in vertex form when it is expressed as f(x) = a(x - h)² + k, highlighting the vertex (h, k) of the parabola.

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What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

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How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 or x - q = 0.