When inequalities are graphed on a coordinate plane, the solutions are located in a region of the coordinate plane, which is represented as a shaded area on the plane. The boundary line for the inequality is drawn as a solid line if the points on the line itself do satisfy the inequality, as in the cases of ≤ and ≥. There are three steps: Rearrange the equation so "y" is on the left and everything else on the right. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>) Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤). If the inequality symbol is ≤ or ≥, then the region includes the parabola, so it should be graphed with a solid line. Otherwise, if the inequality symbol is < or >, the parabola should be drawn with a dotted line to indicate that the region does not include its boundary. Example: Graph the quadratic inequality. We shade above (not below) because y is greater than the other side of the inequality. We draw a dashed line (not solid) because we aren't dealing with an "or equal to" inequality. The dashed line indicates that points on the line are not solutions of the inequality. Follow the steps to solve the problem. Step 1: Multiply the entire first equation by 2. Step 2: Rewrite the system of equations, replacing the first equation with the new equation. Step 3: Add the equations. Step 4: Solve for x. Step 5: Find the y-value by substituting in 3 for x in either equation.
The 4 Inequalities Symbol Words Example > greater than x+3 > 2 < less than 7x < 28 ≥ greater than or equal to 5 ≥ x−1 ≤ less than or equal to 2y+1 ≤ 7
To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y. If the equation is written in the slope-intercept form, plug in the slope and the x and y coordinates for a point on the line to solve for y.
Steps to Solve Get the equation in the form y = ax2 + bx + c. Calculate -b / 2a. This is the x-coordinate of the vertex. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
An inequality says that two values are not equal. a ≠ b says that a is not equal to b. There are other special symbols that show in what way things are not equal. a < b says that a is less than b. a > b says that a is greater than b.
Word Problem Solving Strategies Read through the entire problem. Highlight the important information and key words that you need to solve the problem. Identify your variables. Write the equation or inequality. Solve. Write your answer in a complete sentence. Check or justify your answer.
To graph a parabola, use the coefficient a and coefficient b values from your parabolic equation in the formula x = -b ÷ 2a to solve for x, which is the first coordinate of the vertex. Next, plug x back into your equation to solve for y, which is the second coordinate of the vertex.