Attributes of Quadratics

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 shape does the graph of a quadratic function take?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

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

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), where 'a' and 'b' are the coefficients from the quadratic equation.

Front

What is the Y-intercept of a quadratic function?

Back

The Y-intercept is the point where the graph intersects the Y-axis, found by evaluating f(0) in the quadratic function.

Front

What is the X-intercept of a quadratic function?

Back

The X-intercepts are the points where the graph intersects the X-axis, found by solving the equation f(x) = 0.

Front

What does it mean if a quadratic function has a maximum value?

Back

A maximum value occurs when the parabola opens downwards, indicating that the vertex is the highest point on the graph.

Front

What does it mean if a quadratic function has a minimum value?

Back

A minimum value occurs when the parabola opens upwards, indicating that the vertex is the lowest point on the graph.

Front

What is the standard form of a quadratic function?

Back

The standard form 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 is f(x) = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots or X-intercepts of the function.