Quadratic Systems and Word Problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form 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 maximum height of a projectile modeled by a quadratic equation?

Back

To find the maximum height, use the formula t = -b/(2a) to find the time at which the maximum height occurs, then substitute this time back into the height equation.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

How can you determine if a quadratic equation has real solutions?

Back

By calculating the discriminant (b² - 4ac); if it is greater than or equal to zero, the equation has real solutions.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert, complete the square on the standard form equation.

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 equation x = -b/(2a).

Front

What is a real-world example of a quadratic function?

Back

Projectile motion, such as the height of a ball thrown into the air, can be modeled by a quadratic function.