AE 7.1-7.3 Review

Front

Find the distance between the points (1, 3) and (5, 6).

Back

The distance is 5 units, calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Subtract 3 from both sides to get x² + 6x - 16 = 0.

Front

Calculate the volume of a cylinder with a radius of 5 cm and height of 5 cm using 3.14 for Pi.

Back

The volume is 418.00 cm³, calculated using the formula V = πr²h.

Front

Identify the values of a, b, and c in the quadratic equation 4x² - 8x = 3.

Back

a = 4, b = -8, c = -3.

Front

Use the quadratic formula to solve the equation 2x² + 2x - 12.

Back

The solutions are x = 2 and x = -3.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What does the discriminant of a quadratic equation tell you?

Back

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

Front

What is the formula for the area of a triangle?

Back

The area is A = 1/2 * base * height.

Front

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

Back

Complete the square to rewrite the equation in the form y = a(x - h)² + k.