Math 1 EOC review

Front

What is the formula to find the center of a circle given the endpoints of its diameter?

Back

The center of the circle can be found using the formula: C = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the endpoints of the diameter.

Front

What are the steps to solve a quadratic equation in the form ax² + bx + c = 0?

Back

1. Identify a, b, and c. 2. Calculate the discriminant (D = b² - 4ac). 3. Use the quadratic formula x = (-b ± √D) / (2a) to find the solutions.

Front

What does it mean for a polynomial to be factorable?

Back

A polynomial is factorable if it can be expressed as a product of two or more polynomials of lower degree.

Front

How do you find the axis of symmetry for a quadratic function in the form y = ax² + bx + c?

Back

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

Front

What is the factored form of a perfect square trinomial?

Back

A perfect square trinomial can be factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

Front

What is the vertex of a parabola given in the form y = ax² + bx + c?

Back

The vertex can be found at the point (h, k) where h = -b/(2a) and k = f(h).

Front

What is the discriminant of a quadratic equation and what does it 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 factor the expression x² + 16x + 64?

Back

This expression can be factored as (x + 8)(x + 8), which is a perfect square.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation are the x-intercepts of its graph, where the parabola intersects the x-axis.

Front

What is the standard form of a quadratic function?

Back

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