Quadratic Review

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you convert a quadratic equation to vertex form?

Back

To convert to vertex form, use the formula f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

The 'a' value indicates the direction and width of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What transformation occurs when the 'a' value is greater than 1 in a quadratic function?

Back

The parabola becomes narrower compared to the standard parabola y = x².

Front

What does it mean to complete the square in a quadratic equation?

Back

Completing the square involves rewriting the quadratic in the form (x - p)² = q to find the vertex.

Front

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

Back

Set the quadratic equation to zero and solve for x using factoring, the quadratic formula, or graphing.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

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 x = -b/(2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

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