Mathematics Flashcards
What is the equation of a line in slope-intercept form?
y = mx + b
What is the equation for finding the slope of a line passing through two points (x1, y1) and (x2, y2)?
m = (y2 - y1) / (x2 - x1)
What is the quadratic formula used to solve?
Quadratic equations of the form ax^2 + bx + c = 0
What is the formula for the discriminant of a quadratic equation ax^2 + bx + c = 0?
Discriminant = b^2 - 4ac
What is the formula for finding the vertex of a parabola in standard form ax^2 + bx + c?
Vertex = (-b/2a, f(-b/2a))
What is the formula for finding the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
What is the general form of a linear equation?
Ax + By = C
What is the formula for the distance between two points (x1, y1) and (x2, y2)?
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
What is the formula for the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
What is the formula for finding the x-intercept of a line?
Set y = 0 and solve for x
What is the formula for finding the y-intercept of a line?
Set x = 0 and solve for y
What is the formula for the average rate of change of a function f(x) over the interval [a, b]?
Average rate of change = (f(b) - f(a)) / (b - a)
What is the formula for finding the equation of a circle with center (h, k) and radius r?
(x - h)^2 + (y - k)^2 = r^2
What is the formula for finding the equation of a parabola with focus (h, k + p) and directrix y = k - p?
(x - h)^2 = 4p(y - k)
What is the formula for finding the equation of a hyperbola with center (h, k), vertices (h ± a, k), and foci (h ± c, k)?
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
