Quadratic Functions - All Forms

Front

What is the equation for the axis of symmetry of a quadratic function?

Back

The axis of symmetry is given by the equation x = -\frac{b}{2a}, where a and b are coefficients from the standard form of the quadratic equation ax^2 + bx + c.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r_1)(x - r_2), where r_1 and r_2 are the roots of the quadratic.

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, i.e., f(0) = c in the standard form.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

How do you determine the vertex of a parabola in standard form?

Back

The vertex can be found using the formula ( -\frac{b}{2a}, f(-\frac{b}{2a}) ).

Front

What is the formula for the quadratic formula?

Back

The quadratic formula is x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, used to find the roots of the quadratic equation ax^2 + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by b^2 - 4ac, indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the y-coordinate of the vertex in the vertex form of a quadratic function?

Back

In the vertex form f(x) = a(x-h)^2 + k, the y-coordinate of the vertex is k.