H Algebra II Semester 1 Review

Front

What is the transformation of the function f(x)=x^2 to f(x)=2(x−3)^2−9?

Back

The function undergoes a vertical stretch by a factor of 2, a horizontal shift to the right by 3 units, and a vertical shift down by 9 units.

Front

What value of c makes the expression x^2 - 10x + c a perfect square trinomial?

Back

c = 25, because (x-5)^2 = x^2 - 10x + 25.

Front

How do you solve the equation -x^2 + 6x - 10 = 0 using the Quadratic Formula?

Back

Using the Quadratic Formula, x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, a = -1, b = 6, c = -10, leading to x = 3 \pm i.

Front

Express the inequality -8 ≤ x < 8 in interval notation.

Back

The interval notation is [-8, 8).

Front

What is the result of f(x-2) if f(x) = 2x^2 - 5x + 18?

Back

f(x-2) = 2(x-2)^2 - 5(x-2) + 18 = 2x^2 - 13x + 18.

Front

What is the definition of a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form (a+b)^2 = a^2 + 2ab + b^2 or (a-b)^2 = a^2 - 2ab + b^2.

Front

What does the Quadratic Formula solve?

Back

The Quadratic Formula solves quadratic equations of the form ax^2 + bx + c = 0.

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 of the parabola.

Front

How do you identify the vertex of a parabola from its standard form?

Back

For a quadratic in standard form y = ax^2 + bx + c, the vertex can be found at x = -\frac{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.