Quadratic word problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic equation look like?

Back

The graph of a quadratic equation 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 its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

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 find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, which can be calculated using the vertex formula.

Front

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

Back

The discriminant (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.

Front

How can you determine when an object reaches the ground using a quadratic equation?

Back

Set the height equation h(t) to 0 and solve for t to find when the object is at ground level.

Front

What is the formula for the height of an object in free fall?

Back

The height can be modeled by h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

How do you calculate the time it takes for an object to reach its maximum height?

Back

The time to reach maximum height is found using t = -b/(2a) from the vertex formula of the quadratic equation.

Front

What is the initial height in a quadratic height equation?

Back

The initial height is the value of h when t = 0, represented by the constant term in the quadratic equation.