Quadratic Real World Problems #2

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 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 maximum profit in a quadratic profit function?

Back

To find the maximum profit, calculate the vertex of the quadratic function using the formula x = -b/(2a), where a and b are coefficients from the profit function.

Front

What is the significance of the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x where the function equals zero, indicating the points where the graph intersects the x-axis.

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 does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: 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 the time it takes for an object to hit the ground using a quadratic function?

Back

Set the height function h(t) to zero and solve for t to find the time when the object reaches ground level.

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

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

How do you interpret the coefficients in a quadratic function?

Back

The coefficient 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.