
Define rate of change and slope, with average rate as delta y over delta x and slope as y2−y1 over x2−x1; cover positive, negative, zero, and undefined slopes.
determine factorization eligibility with the discriminant d = b^2 - 4ac. if d is a perfect square, factorize; if not, use another method, noting real versus complex roots.
Use the discriminant to identify distinct roots. When D > 0, two distinct roots exist, as shown by x^2 - x - 12 = 0: roots 4 and -3.
Apply the Pythagorean theorem to a 45-45-90 isosceles triangle to find the hypotenuse as x√2, and relate side lengths using coefficients, with sohcahtoa guidance.
Explore trigonometry of spatial angles by proving 45-45-90 in an isosceles right triangle and using sohcahtoa to derive sin 45 = cos 45 = sqrt2/2 and tan 45 = 1.
Learn to use the Pythagorean theorem to solve for a side of a right triangle by identifying the hypotenuse and applying c^2 = a^2 + b^2.
Identify outliers in a data set by using the interquartile range: bound data with Q1 minus 1.5 IQR and Q3 plus 1.5 IQR, as shown with 54 as an outlier.
Determine the side length of an equilateral triangle from its area using the formula area equals (l^2 sqrt3)/4. Conclude with l about 6.1 cm.
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