Algebra Semester Review Part 1 24-25

Front

Evaluate f(x)= 2x² + 5x - 17 for f(-1)

Back

f(-1) = 2(-1)² + 5(-1) - 17 = 2(1) - 5 - 17 = 2 - 5 - 17 = -20

Front

The function h(t) = -16t² + 48t represents the height of a stone t seconds after it is thrown. Evaluate h(0.35) to find the height of the stone after 0.35 seconds.

Back

h(0.35) = -16(0.35)² + 48(0.35) = -16(0.1225) + 16.8 = -1.96 + 16.8 = 14.84 seconds

Front

Which relation is NOT a function? {(1,-5), (3,1), (-5,4), (4,-2)}, {(2,7), (3,7), (4,7), (5,8)}, {(1,-5), (-1,6), (1,5), (6,-3)}, {(3,-2), (5,-6), (7,7), (8,8)}

Back

The relation {(1,-5), (-1,6), (1,5), (6,-3)} is NOT a function because the input 1 corresponds to two different outputs (-5 and 5).

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What is the vertex form of a quadratic function?

Back

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

Front

Evaluate f(x) = 3x² - 4 for f(2)

Back

f(2) = 3(2)² - 4 = 3(4) - 4 = 12 - 4 = 8.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

Evaluate f(x) = x² - 3x + 2 for f(1)

Back

f(1) = (1)² - 3(1) + 2 = 1 - 3 + 2 = 0.

Front

What is the axis of symmetry for the quadratic function f(x) = ax² + bx + c?

Back

The axis of symmetry is given by the formula x = -b/(2a).