ORCA Midterm Review

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you find the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a). Substitute this x-value back into the equation to find the y-coordinate.

Front

What does the discriminant of a quadratic equation tell us?

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

What is the formula for the area of a triangle?

Back

The area of a triangle is given by A = 1/2 * base * height.

Front

How do you solve an absolute value equation like |x + 3| = 5?

Back

To solve |x + 3| = 5, set up two equations: x + 3 = 5 and x + 3 = -5. Solve each for x.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction.

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

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL) and remember that i² = -1.

Front

What is the sum of the roots of a quadratic equation in standard form?

Back

The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -b/a.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions are the values that satisfy all equations simultaneously.