ADV TOP MATH
Graphing a Quadratic Equation in Vertex Form
*Determine the vertex point (h,k) and graph it. *Graph the axis of symmetry. *Choose two x-values on the side of the axis of symmetry closest to the origin and determine the points. *Use symmetry to graph the two points on the other side of the axis of symmetry. *Connect the points.
Steps for Graphing a Quadratic Equation in Standard Form
*Determine if the graph will open up or down. •Opens up if "a" is positive (the vertex point will be the minimum point). •Opens down if "a" is negative (the vertex point is the maximum point). 1.Find the vertex point. •Find the x-value by x = -b/(2a). •Find the y-value by substituting the x-value into the equation and solving for "y". 3. Find more points to determine the graph. •Choose two integers larger than the x-value of the vertex point. •Choose two integers smaller than the x-value of the vertex point. •Substitute these values in place of "x" in the equation and solve for "y". •Four ordered pairs have been found. 4. Graph and connect all points that have been found.
6.5 Systems of equations by elimination
Step 1 Try to eliminate a variable as you add the left sides and the right sides of the two equations Step 2 Set the sum resulting from adding the left sides equal to the sum resulting from adding the right sides Step 3 Solve for the variable that was not cancelled or eliminated Step 4 Use the answer found in step 3 to solve for the other variable by substituting this value in one of the two equations
6.7 Linear Programming
Step 1. Define variables. Step 2. Write a system of inequalities. Step 3. Graph the system of inequalities. Step 4. Find the coordinates of the vertices of the feasible region. Step 5. Write an expression to be maximized or minimized. Step 6. Substitute the coordinates of the vertices in the expression. Step 7. Select the greatest or least result to answer the problem.
6.6 System of linear inequalities graphically we will follow these steps:
Step 1. Solve the inequality for y. Step 2. Treat the inequality as a linear equation and graph the line as either a solid line or a dashed line depending on the inequality sign. a. If the inequality sign does not contain an equals sign (< or >) then draw the line as a dashed line. b. If the inequality sign does have an equals sign (≤ or ≥) then draw the line as a solid line. Step 3. Shade the region that satisfies the inequality Step 4. Repeat steps 1 - 3 for each inequality Step 5. The solution set will be the overlapped region of all the inequalities
6.3 Systems of equations by graphing
Step 1: Place the linear equations in slope-intercept form. Step 2: Graph the lines and use the graph to find the common point. Step 3: Check your answer and present it as an ordered pair. Accuracy here is important, use graph paper and a straight edge when using the graphing method to solve linear systems.
6.2 Solving Slope-Intercept & Point-Slope Equations
Step 1: Put the equation in Slope Intercept Form. Step 2: Graph the y-intercept point (the number in the b position) on the y-axis. ... Step 3: From the point plotted on the y-axis, use the slope to find your second point. ... Step 4: Draw your line using the two points you plotted (y-intercept (b) first, slope (m) second.
6.8 Graphing quadratics
Terms: 1. Parabola - the graph of a quadratic equation, which is u-shaped 2. Vertex Point - it's the highest or lowest point on the graph 3. Axis of Symmetry - the vertical line that goes through the vertex point 4. Standard Form - y = ax² + bx + c 5. Vertex Form - y = a(x - h)² + k
6.4 Systems of equations by substitution
The substitution method is most useful for systems of 2 equations in 2 unknowns. The main idea here is that we solve one of the equations for one of the unknowns, and then substitute the result into the other equation. Substitution method can be applied in four steps Step 1: Solve one of the equations for either x = or y = . Step 2: Substitute the solution from step 1 into the other equation. Step 3: Solve this new equation. Step 4: Solve for the second variable.
