Quadratic Word Problems

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by: ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

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

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x = 0. It represents the initial value of the function.

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept, substitute x = 0 into the quadratic equation and solve for y.

Front

What does the x-intercept of a quadratic function represent?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, representing the values of x for which the function equals zero.

Front

How can you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant of a quadratic equation indicate?

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

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, which can be calculated using the vertex formula.