I can plot a quadratic graph I can draw up a table from the equation with no problems (Yes/need more work/No) I can fill up a table by substituting values of x in each row and then adding the columns to find the corresponding values of y From the table, I know which two values I need to plot I know how to plan where to draw the axes according to my values of x and y (Yes/need more work/No) I know how to plot the points and join to form the curve

Notice the ‘symmetry’ in the numbers 𝒚= 𝒙 𝟐 +𝒙−𝟔 𝒙 -4 -3 -2 -1 1 2 3 𝒙 𝟐 +𝒙 -6 𝒚 = 𝒙 𝟐 +𝒙−𝟔 (−4) 2 16 9 (−3) 2 4 (−2) 2 (−1) 2 1 (0) 2 1 (1) 2 4 (2) 2 9 (3) 2 −4 −3 −2 −1 1 2 3 12 6 2 2 6 12 −6 −6 −6 −6 −6 −6 −6 −6 6 −4 −6 −6 −4 6 Notice the ‘symmetry’ in the numbers

Notice the ‘symmetry’ in the numbers 𝒚=𝟔− 𝒙 𝟐 𝒙 -3 -2 -1 1 2 3 𝟔 − 𝒙 𝟐 𝒚 = 𝟔− 𝒙 𝟐 6 6 6 6 6 6 6 − (−1) 2 − (−0) 2 −92 −(−3) 2 −42 − (−2) 2 −12 02 −12 − (1) 2 −42 − (2) 2 −92 − (3) 2 −3 2 5 6 5 2 −3 Notice the ‘symmetry’ in the numbers

Notice the ‘symmetry’ in the numbers 𝒚= 𝟐𝒙 𝟐 +𝟐𝒙−𝟗 𝒙 -3 -2 -1 1 2 𝟐 𝒙 𝟐 +𝟐𝒙 -9 𝒚 = 2 𝒙 𝟐 +𝟐𝒙−𝟗 18 2(9) 2(−3) 2 8 2(4) 2(−2) 2 2(1) 2 2(−1) 2 2(0) 2(0) 2 2 2(1) 2(1) 2 8 2(4) 2 (2) 2 2(0) −6 2(−3) −4 2(−2) −2 2(−1) 2 2(1) 2(2) 4 4 4 12 12 −9 −9 −9 −9 −9 −9 3 −5 −9 −9 −5 3 Notice the ‘symmetry’ in the numbers

Notice the ‘symmetry’ in the numbers 𝒚= −𝒙 𝟐 −𝟐𝒙+𝟏𝟎 𝒙 -5 -4 -3 -2 -1 1 2 3 − 𝒙 𝟐 −𝟐𝒙 +10 𝒚 = − 𝒙 𝟐 −𝟐𝒙+𝟏𝟎 −25 −(−5) 2 −16 −(−4) 2 −9 −(−3) 2 −4 −(−2) 2 −1 −(−1) 2 −(0) 2 −1 −(1) 2 −4 −(2) 2 −(3) 2 −9 10 −2(−5) 8 −2(−4) 6 −2(−3) 4 −2(−2) 2 −2(−1) −2(0) −2 −2(1) −4 −2(2) −6 −2(3) +10 +10 +10 +10 +10 +10 +10 +10 +10 −5 2 7 10 11 10 7 2 −5 Notice the ‘symmetry’ in the numbers

To be able to plot a system of graphs

Plotting a linear graph & a quadratic graph When a straight line graph and a quadratic graph are plotted on the same axes, we call it a system of linear and quadratic graphs They can meet at: 2 points 1 point No point The points where they meet are called points of intersection

Points of Intersection Points of intersection are those points where the graphs are equal to each other In this example, the graphs drawn are: 𝒚= 𝒙 𝟐 −𝟓𝒙+𝟕 𝒚=𝟐𝒙+𝟏 At the points of intersection (1,3) and (6,13) the graphs are equal 𝒙 𝟐 −𝟓𝒙+𝟕=𝟐𝒙+𝟏 𝑥=1 𝑜𝑟 𝑥=6 Let us see an example on Geogebra You can solve a complicated looking equation by drawing two graphs and reading their POIs

CW/HW A) Plot these two graphs: Linear Graph  𝒚=𝟒 Quadratic Graph  𝒚= 𝒙 𝟐 +𝟑𝒙 (𝒙 values : -5 to 2) Write down the points of intersection B) Plot these two graphs: Linear Graph  𝒚=𝒙−𝟐 Quadratic Graph  𝒚= 𝒙 𝟐 −𝟒𝒙−𝟐 (𝒙 values : -2 to 6) C) Plot these two graphs: Linear Graph  𝒚=−𝒙+𝟏 Quadratic Graph  𝒚= 𝒙 𝟐 +𝒙−𝟐 (𝒙 values: -4 to 3) CW/HW