Alg Quadratic Applications

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola (opening upwards or downwards).

Front

How do you find the x-coordinate of the vertex of a quadratic function?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients from the quadratic equation ax² + bx + c.

Front

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

Back

The discriminant (D = b² - 4ac) determines 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.

Front

How can you determine when an object launched from the ground will hit the ground using a quadratic function?

Back

Set the height function equal to zero and solve for t. This gives the time(s) when the object is at ground level.

Front

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

Back

The height h(t) of an object in free fall can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What does the initial height of an object represent in a quadratic function?

Back

The initial height is represented by the constant term (c) in the quadratic function, indicating the height of the object at time t = 0.

Front

How do you find the maximum height of an object launched vertically?

Back

To find the maximum height, calculate the vertex of the height function using x = -b/(2a) to find the time at which the maximum height occurs, then substitute that time back into the height function.

Front

What is the area of a rectangle in terms of its length and width?

Back

The area A of a rectangle is given by the formula A = length × width.

Front

How do you set up an equation to find the dimensions of a rectangular garden given its area?

Back

If the length is L and the width is W, set up the equation L × W = area, and use any additional relationships (e.g., L = W + 10) to solve for L and W.