Chapter 1 Review (HA2)

Front

What is completing the square in algebra?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, which makes it easier to solve for x.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots of the equation: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

How do you find the maximum height of a projectile?

Back

To find the maximum height of a projectile, use the vertex formula t = -b/(2a) from the quadratic equation h(t) = at² + bt + c, where a is negative for downward-opening parabolas.

Front

What is a polynomial equation?

Back

A polynomial equation is an equation that involves a polynomial expression, which is a sum of terms consisting of variables raised to non-negative integer powers and coefficients.

Front

What does it mean for a polynomial to have complex roots?

Back

Complex roots occur when the discriminant of a polynomial is negative, resulting in roots that include imaginary numbers, typically expressed in the form a + bi.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you solve a cubic equation?

Back

Cubic equations can be solved using various methods, including factoring, synthetic division, or applying the cubic formula, which is more complex than the quadratic formula.

Front

What is the significance of the vertex in a quadratic function?

Back

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

Front

What is the formula for the height of a projectile?

Back

The height of a projectile can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What is the role of coefficients in a polynomial?

Back

Coefficients are the numerical factors in a polynomial that multiply the variable terms, determining the shape and position of the graph.