Quadratic Word Problems

How do you graph a quadratic function?

• Find the vertex, axis of symmetry, and intercepts, then plot these points and draw a smooth curve through them.

• Only plot the vertex and draw a straight line through it.

• Use only the intercepts to create a graph without considering the vertex.

• Draw a random curve without any calculations.

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

• Set the height function equal to zero and solve for t.

• Calculate the object's initial velocity and multiply by time.

• Use the quadratic formula to find the maximum height.

• Determine the object's weight and divide by gravity.

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

• It represents the maximum value of the function.

• It is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

• It indicates the direction of the parabola's opening.

• It shows the 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 represented by a straight line

• A function that has no real roots

What is the factored form of a quadratic function and when is it useful?

• f(x) = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots. It is useful for quickly identifying the x-intercepts of the graph.

• f(x) = ax² + bx + c, which is useful for finding the vertex of the parabola.

• f(x) = a(x + r₁)(x + r₂), where r₁ and r₂ are the roots. It is useful for determining the maximum value of the function.

• f(x) = a(x - r₁)(x + r₂), which is useful for solving inequalities.

What does the vertex of a parabola represent in a quadratic function?

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

• The maximum or minimum point of the quadratic function, depending on the direction of the parabola (opening upwards or downwards).

• The average value of the function over a given interval.

• The point of symmetry for the parabola.

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

• It determines the width of the parabola.

• It determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

• It affects the position of the vertex of the parabola.

• It indicates the number of real roots of the quadratic equation.

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 formula x = -b/(2a).

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

• A diagonal line that passes through the origin of the graph.

• A line that represents the maximum or minimum value of the quadratic function.

What is the maximum height of a projectile launched with an initial velocity?

• h = -16t² + vt + h₀

• h = 16t² + vt + h₀

• h = vt - 16t²

• h = vt + 16t²

What is the standard form of a quadratic equation?

• ax² + bx + c = 0

• ax² - bx + c = 0

• ax² + b + c = 0

• ax² + bx = 0