Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Identify the standard form of a quadratic equation.

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What are the values of a, b, and c in the equation 4x² - 8x - 3 = 0?

Back

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

Front

Which of the following is a quadratic function: f(x) = -3x², f(x) = -5x - x², y = 3x³ - 4x + 5, or y = 3x² - 5?

Back

f(x) = -3x², f(x) = -5x - x², and y = 3x² - 5 are quadratic functions. y = 3x³ - 4x + 5 is NOT a quadratic function.

Front

How can you determine if a quadratic equation opens upward or downward?

Back

If the coefficient of x² (a) is positive, the graph opens upward. If a is negative, the graph opens downward.

Front

What is the y-intercept of the quadratic function y = x² - 3x + 5?

Back

The y-intercept is (0, 5).

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant indicates the number of solutions (roots) of the quadratic equation. It is calculated as b² - 4ac.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upward or downward.

Front

How do you find the x-intercepts of a quadratic equation?

Back

To find the x-intercepts, set y = 0 and solve the quadratic equation ax² + bx + c = 0.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).