Quadratic Real World Problems #2

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 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

What are the roots of a quadratic equation?

Back

The roots (or solutions) of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the vertex of a parabola?

Back

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

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 parabola, which occurs at t = -b/(2a) in the function h(t) = at² + bt + c.

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 when an object hits the ground using a quadratic function?

Back

To find when an object hits the ground, set the height function h(t) equal to zero and solve for t.

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, found by evaluating the function at t = 0.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.