A line of best fit is a straight line drawn through the middle of the points on a scatter plot. It shows the overall trend of the data. You can write its equation in slope-intercept form, y = mx + b, and use it to make predictions. It is also called a trend line or line of fit.
A scatter plot is a graph of paired data, with one point for each pair. Correlation describes how the two variables move together. If the points rise from left to right, the correlation is positive. If they fall, it is negative. If there is no pattern, there is no correlation.
A two-way table shows data about two categories at once, like grade level and homework choice. Each row is one group, and each column is another. The cells inside show how many fit both. You can use the table to find percents and to see if the two categories are related.
Linear, quadratic and exponential models are three common ways to describe data. To choose one from a table, look at how y changes as x goes up by the same step. Equal first differences mean linear. Equal second differences mean quadratic. Equal ratios mean exponential. Then write the equation and use it to predict.
A linear-quadratic system is a line and a parabola, like y = x² − 1 and y = x + 1. Its solutions are the points where the two graphs cross. To solve it, set the two expressions for y equal, solve the quadratic, then find each y. A system can have two, one or no solutions.
The discriminant is b² − 4ac, the part under the square root in the quadratic formula. It tells you how many real solutions ax² + bx + c = 0 has, without solving it. If it is positive, there are two. If it is zero, there is one. If it is negative, there are none.
The quadratic formula solves any quadratic equation ax² + bx + c = 0. The solutions are x = (−b ± √(b² − 4ac)) / 2a. Put the equation in standard form, find a, b and c, and plug them in. It works even when the quadratic won’t factor. The answers are where the graph crosses the x-axis.
Completing the square is a way to solve a quadratic by turning one side into a perfect square trinomial. For x² + bx, add (b/2)² to both sides. Then x² + bx + (b/2)² = (x + b/2)², and you can solve with square roots. It works for every quadratic.
Solving quadratics with square roots works when the equation has a squared term and no x-term, like x² = 25 or (x − 3)² = 16. Isolate the squared part, then take the square root of both sides. Use ± because both a positive and a negative number square to the same value.
Solving quadratic equations by factoring uses the zero product property: if ab = 0, then a = 0 or b = 0. Set the equation equal to 0, factor the quadratic, then set each factor equal to 0 and solve. For example, x² + 5x + 6 = 0 becomes (x + 2)(x + 3) = 0, so x = −2 or x = −3.