Quadratic Equation Word Problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the standard forms of a quadratic equation?

Back

The standard forms are: 1) Standard form: ax² + bx + c = 0; 2) Vertex form: y = a(x - h)² + k; 3) Factored form: y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form ax² + bx + c = 0, factor it into (px + q)(rx + s) = 0, and set each factor to zero to find the roots.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula (h, k) from the vertex form of the equation.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How can you model real-world situations using quadratic equations?

Back

Quadratic equations can model various real-world situations such as projectile motion, area problems, and profit maximization by relating variables in a parabolic relationship.

Front

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

Back

The maximum height can be found at the vertex of the parabola, which occurs at x = -b/(2a). Substitute this x value back into the equation to find the height.