Key Features 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 does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

How do you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by determining the vertex of the quadratic function, which occurs at x = -b/(2a). The y-value at this x-coordinate gives the maximum height.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of the function when x = 0.

Front

What does the term 'increasing interval' refer to in the context of a quadratic function?

Back

The increasing interval refers to the range of x-values over which the function's output (y-value) is increasing, typically found to the left of the vertex for a parabola that opens upwards.

Front

What does the term 'decreasing interval' refer to in the context of a quadratic function?

Back

The decreasing interval refers to the range of x-values over which the function's output (y-value) is decreasing, typically found to the right of the vertex for a parabola that opens upwards.

Front

How can you determine the minimum value of a quadratic function?

Back

The minimum value can be determined by finding the vertex of the quadratic function, which gives the lowest point on the graph for a parabola that opens upwards.

Front

What is the standard form of a quadratic function?

Back

The standard 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 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 the equation x = -b/(2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.