4.70: Quadratic Regression

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, 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.

Front

How can you determine the number of real solutions of a quadratic equation?

Back

The number of real solutions can be determined using the discriminant (b² - 4ac). If the discriminant is positive, there are two real solutions; if it is zero, there is one real solution; if negative, there are no real solutions.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

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 formula x = -b/(2a).

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found by evaluating the function at the vertex, which occurs at x = -b/(2a).

Front

What is a projectile motion equation?

Back

A projectile motion equation is a quadratic function that models the height of an object in motion under the influence of gravity, typically in the form h(t) = -16t² + vt + h₀.

Front

What does the term 'initial velocity' refer to in projectile motion?

Back

Initial velocity refers to the speed at which an object is launched or thrown at the beginning of its motion.

Front

What is the meaning of the term 'maximum height' in the context of projectile motion?

Back

Maximum height is the highest point reached by a projectile during its flight, which corresponds to the vertex of the parabola in its height vs. time graph.