Math 2-Unit 2 Midterm Review Day 2

Front

What is the standard form of a quadratic function?

Back

f(x) = ax² + bx + c

Front

What is the axis of symmetry of the quadratic function y = (x - 2)² + 3?

Back

x = 2

Front

What is the factored form of y = x² - 9x + 14?

Back

(x - 7)(x - 2)

Front

What is the vertex form of a quadratic function?

Back

f(x) = 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 x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What does the discriminant tell you about a quadratic equation?

Back

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

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

If the roots are r1 and r2, then a(x - r1)(x - r2) = ax² - a(r1 + r2)x + ar1r2.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

How do you convert from vertex form to standard form?

Back

Expand f(x) = a(x - h)² + k to get f(x) = ax² - 2ahx + (ah² + k).