Semester Review

Front

What are the solutions of the quadratic function with factors (x+3)(x-9)?

Back

-3 and 9

Front

Which quadratic function has solutions x = -15 and x = 15?

Back

f(x) = x^2 - 225

Front

What is the interval notation represented by the graph that includes all values less than -16 and greater than 2?

Back

(-∞, -16] ∪ [2, ∞)

Front

Identify the values of a, b, and c in the quadratic equation 4x² - 8x = 3.

Back

a = 4, b = -8, c = -3

Front

Convert the quadratic equation y = -x² + 10x - 4 to vertex form.

Back

y = -(x - 5)² + 21

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

Use the formula h = -b/(2a) to find the x-coordinate, then substitute h back into the function to find k.

Front

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

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

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

Back

Standard form is written as f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you convert from standard form to vertex form?

Back

Complete the square on the quadratic expression.