Quadratic Functions in Factored form

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is expressed as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the function.

Front

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

Back

To find the y-intercept, set x = 0 in the function and solve for f(0).

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) in the vertex form f(x) = a(x - h)² + k.

Front

How do you determine the vertex from the factored form?

Back

The vertex can be found by averaging the x-coordinates of the roots (r1 and r2) and substituting this value back into the function to find the corresponding y-coordinate.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

How do you find the roots of a quadratic function in factored form?

Back

Set the factored form equal to zero and solve for x: a(x - r1)(x - r2) = 0, giving roots r1 and r2.

Front

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

Back

The leading 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 convert from standard form to factored form?

Back

To convert from standard form f(x) = ax² + bx + c to factored form, you can use factoring techniques or the quadratic formula to find the roots.

Front

What is the y-intercept of the function f(x) = (x - 3)(x + 4)?

Back

The y-intercept is (0, -12), found by substituting x = 0 into the function.