Quadratic Word Problems

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form can be found using the formula: x = -b/(2a). The y-coordinate can be found by substituting x back into the function.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. If the parabola opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

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

How do you determine the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How can you model real-world situations using quadratic functions?

Back

Quadratic functions can model various real-world situations, such as projectile motion, profit maximization, and area problems, where relationships are parabolic.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0 (f(0) = c).