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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA-REI.B.4B