PreCalc Honors Review on Sections 2.1-2.3

Front

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.

Front

How do you find the vertex of the quadratic function f(x) = -x² - 4x + 12?

Back

To find the vertex, rewrite the function in vertex form. Completing the square gives f(x) = -1(x + 2)² + 16, so the vertex is (-2, 16).

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function f(x) = ax² + bx + c is the value of f(0), which is c.

Front

Find the y-intercept of f(x) = 2x² - 2x + 1.

Back

The y-intercept is f(0) = 2(0)² - 2(0) + 1 = 1.

Front

What is the end behavior of the graph of a quadratic function?

Back

For a quadratic function f(x) = ax² + bx + c, if a > 0, as x → ±∞, f(x) → ∞. If a < 0, as x → ±∞, f(x) → -∞.

Front

Rewrite f(x) = x² - 8x + 1 in vertex form.

Back

Completing the square gives f(x) = (x - 4)² - 15.

Front

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

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you perform polynomial long division?

Back

To perform polynomial long division, divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by this result, subtract, and repeat with the new polynomial.

Front

Solve using long division: (8x² + 6x - 20) ÷ (4x - 5).

Back

The result is 2x + 4.

Front

What is the formula for the axis of symmetry of a quadratic function?

Back

The axis of symmetry for a quadratic function f(x) = ax² + bx + c is given by x = -b/(2a).