Midterm Practice #3 ORCA

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What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

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Back

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What does it mean when an equation has no solution?

Back

An equation has no solution when there are no values that satisfy the equation, often resulting from contradictory statements.

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Factor the expression: 25x^2 - 9.

Back

The factored form is (5x + 3)(5x - 3).

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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What is the difference between a solution and a root in mathematics?

Back

A solution refers to the value(s) that satisfy an equation, while a root specifically refers to the value(s) that make a polynomial equal to zero.

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What is the principle of factoring in algebra?

Back

Factoring involves rewriting an expression as a product of its factors, which can simplify solving equations.

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What does it mean for an inequality to be 'strict'?

Back

A strict inequality uses < or >, meaning the values cannot be equal, unlike non-strict inequalities (≤ or ≥) which allow equality.

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

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, indicating the maximum or minimum value.