Quadratics

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

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

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 ax² + bx + c.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.

Front

What does the 'a' value in a quadratic function determine?

Back

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

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.

Front

How can you convert a quadratic function from standard form to vertex form?

Back

You can convert to vertex form by completing the square: f(x) = a(x - h)² + k.

Front

What is the formula for the vertex of a parabola given in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

What is the effect of changing the 'b' value in a quadratic function?

Back

Changing the 'b' value affects the position of the vertex and the axis of symmetry, but does not change the direction of the parabola.