Intro to Quadratic Applications

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 vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

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.

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, which occurs when x = 0. It is found by evaluating f(0).

Front

What does the term 'maximum height' refer to in the context of projectile motion?

Back

Maximum height refers to the highest point reached by an object in projectile motion, which corresponds to the vertex of the quadratic function modeling its height.

Front

What is the formula for the height of an object in projectile motion?

Back

The height h(t) of an object in projectile motion 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 is the meaning of 'positive zero' in the context of quadratic functions?

Back

A positive zero refers to the positive x-intercept of the quadratic function, which is the point where the graph intersects the x-axis.

Front

How can you determine how long it takes for an object to hit the ground using a quadratic function?

Back

To determine how long it takes for an object to hit the ground, set the height function equal to zero and solve for t.

Front

What is the role of the coefficient 'a' in a quadratic function?

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 does the term 'discriminant' refer to in quadratic equations?

Back

The discriminant, given by the formula 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.