Cumulative Review-1st Semester Algebra 2

Front

Complete the square for the expression: x^2 + 14x + ____

Back

x^2 + 14x + 49

Front

Describe the transformations of the function f(x) = -2x^2 + 4 compared to the parent function f(x) = x^2.

Back

Vertical Stretch by 2, Reflection over x, Up 4

Front

Solve the inequality: 2x^2 + 5x ≥ 12

Back

(−∞, -4] U [1.5, ∞)

Front

How is the graph transformed when f(x) = x^2 is changed to f(x) = - (x + 3)^2 + 2?

Back

3 units left, 2 units up, reflected across the x-axis

Front

Factor the expression: 9x^2 - 25

Back

(3x - 5)(3x + 5)

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

Front

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

Back

Standard form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the axis of symmetry for the quadratic function f(x) = ax^2 + bx + c?

Back

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

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you find the x-intercepts of a quadratic function?

Back

Set f(x) = 0 and solve the equation ax^2 + bx + c = 0.