Quadratics

Front

What is a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation in standard form.

Front

What does the 'a' value in a quadratic equation represent?

Back

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

Front

What does the 'b' value in a quadratic equation represent?

Back

The 'b' value affects the position of the vertex along the x-axis and the axis of symmetry.

Front

What does the 'c' value in a quadratic equation represent?

Back

The 'c' value represents the y-intercept of the parabola, which is the point where the graph crosses the y-axis.

Front

How do you determine the vertex from a quadratic equation in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h), the value of the function at h.

Front

What is the formula for the vertex of the parabola y = ax² + bx + c?

Back

The vertex is given by the coordinates (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

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