Quadratic Functions Word Problems

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

• It determines the direction of the parabola and affects its width.

• It represents the y-intercept of the function.

• It indicates the maximum value of the function.

• It determines the number of roots of the quadratic equation.

What is a quadratic function?

• A polynomial function of degree 1

• 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.

• A linear function that graphs to a straight line

• A function that has a constant value regardless of the input

What is the difference between maximum and minimum in the context of quadratic functions?

• Maximum refers to the highest point of the parabola (if it opens downwards), while minimum refers to the lowest point (if it opens upwards).

• Maximum is the lowest point of the parabola, while minimum is the highest point.

• Maximum and minimum refer to the same point on the parabola regardless of its direction.

• Maximum is the point where the parabola intersects the x-axis, while minimum is where it intersects the y-axis.

What is the axis of symmetry in a quadratic function?

• A vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

• A horizontal line that intersects the vertex of the parabola.

• The point where the parabola touches the x-axis.

• A diagonal line that runs from the vertex to the x-axis.

What does it mean for a quadratic function to be in vertex form?

• A quadratic function is in vertex form when it is expressed as f(x) = a(x - h)² + k, highlighting the vertex (h, k) directly.

• A quadratic function is in vertex form when it is expressed as f(x) = ax² + bx + c, showing the standard form.

• A quadratic function is in vertex form when it is expressed as f(x) = a(x + h)² + k, indicating the vertex at (-h, k).

• A quadratic function is in vertex form when it is expressed as f(x) = a(x - h)(x - k), representing the roots.

How do you find the maximum height of an object modeled by a quadratic function?

• By calculating the vertex of the parabola using the formula t = -b/(2a) and substituting this value back into the function.

• By finding the roots of the quadratic equation and averaging them.

• By using the quadratic formula to solve for the maximum height directly.

• By graphing the function and identifying the highest point visually.

How do you determine if a quadratic function has a maximum or minimum?

• If 'a' is positive, the function has a maximum; if 'a' is negative, the function has a minimum.

• If 'a' is positive, the function has a minimum; if 'a' is negative, the function has a maximum.

• The function has a maximum if the vertex is above the x-axis.

• The function has a minimum if the vertex is below the x-axis.

What is the significance of the y-intercept in a quadratic function?

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

• The y-intercept represents the maximum value of the function.

• The y-intercept indicates the slope of the function at x = 0.

• The y-intercept is the point where the graph intersects the x-axis.

What does the graph of a quadratic function look like?

• A straight line

• A circle

• A parabola

• A hyperbola

What are the roots of a quadratic function?

• The values of x for which the function f(x) = 0, representing the points where the graph intersects the x-axis.

• The coefficients of the quadratic equation that determine its shape.

• The maximum or minimum points of the quadratic function.

• The values of x that make the function undefined.