Quadratic Review

Front

What are the coefficients in the quadratic equation 3x² + 4 = 5x?

Back

a = 3, b = -5, c = 4

Front

How do you find the zeros of the equation (x+10)(x-2) = 0?

Back

Set each factor to zero: x + 10 = 0 or x - 2 = 0, giving zeros at x = -10 and x = 2.

Front

What is another term for the x-intercepts of a quadratic function?

Back

Zeros

Front

What is the formula for the axis of symmetry in a quadratic equation?

Back

x = -b/(2a)

Front

How do you find the x-intercepts of the function y = x² - 3x - 10?

Back

Factor the equation or use the quadratic formula to find x = 5 and x = -2.

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c

Front

What does the 'a' coefficient in a quadratic equation determine?

Back

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

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b/(2a) and k is the function value at h.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

By looking at the sign of the coefficient 'a': if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the quadratic formula used for?

Back

To find the roots (or zeros) of a quadratic equation: x = (-b ± √(b² - 4ac)) / (2a).