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 represents the value of the function at that point.

Front

What does the positive x-intercept indicate in a quadratic function?

Back

The positive x-intercept indicates the points where the graph crosses the x-axis, representing the values of x for which the function equals zero.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax² + bx + c = 0.

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, and it passes through the vertex.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Front

What is the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found at the vertex of the parabola, specifically the y-coordinate of the vertex.

Front

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

Back

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