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# Graphing y = ax^2 + bx + c

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### Graphing y = ax^2 + bx + c

1. 1. Graphing y = ax2 + bx + cBy L.D.
2. 2. Table of Contents Slide 3: Formula Slide 4: Summary Slide 5: How to Find the the Direction the Graph Opens Towards Slide 6: How to Find the y Intercept Slide 7: How to Find the Vertex Slide 8: How to Find the Axis of Symmetry Slide 9: Problem 1 Slide 16: Problem 2 Slide 22: End
3. 3. Formula y = ax2 + bx + c
4. 4. SummaryIn this presentation we are learning how to graphy = ax2 + bx + c. We will graph this by first findingthe direction it opens up, the y intercept, the vertexand the axis of symmetry. The next three slides aredevoted to how to find these.
5. 5. How to Find the the Directionthe Graph Opens Towards y = ax2 + bx + c Our graph is a parabola so it will look like or In our formula y = ax2 + bx + c, if the a stands for a number over 0 (positive number) then the parabola opens upward, if it stands for a number under 0 (negative number) then it opens downward.
6. 6. How to Find the y Intercept y = ax2 + bx + c The y intercept is a number that is not generally used as a vertex, it is used as one of the places to plot the line. It’s formula is (0, c). The c is always a constant. The exception to it not being used as a vertex is when the b is equal to 0.
7. 7. How to Find the Vertex y = ax2 + bx + c The vertex has an x coordinate of –b/2a To find the y coordinate one must place the x coordinate number into the places x occupies in the problem.
8. 8. How to Find the Axis ofSymmetry y = ax2 + bx + c The line for the axis of symmetry crosses over the number achieved by doing the formula –b/2a.
9. 9. Problem 1 Formula: y = ax2 + bx + c y = 5x2 + 10x – 3 Directions: find the vertex, y-intercept and axis of symmetry. Then you may graph.
10. 10. Problem 1 Formula: y = ax2 + bx + c y = 5x2 + 10x – 3 The first thing we will find is the vertex. As mentioned in slide 6, this is done by first finding the x coordinate using –b/2a. –b/2a = -10/2(5) = -10/10 = -1 Our x coordinate is -1. On the next slide we will find the y coordinate.
11. 11. Problem 1 Formula: y = ax2 + bx + c y = 5x2 + 10x – 3 x coordinate: -1 As mentioned in slide 6, the y coordinate is found by placing the x coordinate in the places that x occupies in the problem.y = 5(-1)2 + 10(-1) – 3y = 5 + - 10 – 3y = -8, so our y coordinate is -8, making our vertexlocated at (-1, -8).
12. 12. Problem 1 Formula: y = ax2 + bx + c y = 5x2 + 10x – 3 Vertex: (-1, -8) Now we need to find the axis of symmetry, to do this we would use the same formula (–b/2a) as we used to get our x coordinate, so our axis of symmetry is -1.
13. 13. Problem 1 Formula: y = ax2 + bx + c y = 5x2 + 10x – 3 Vertex: (-1, -8) Axis of symmetry: -1 The last step before graphing is where we need to find our y-intercept which will be the place that our vertex reaches too. We will do this by going to slide 6. The formula it gives us is (0, c), so our y-intercept is (0, -3).
14. 14. Problem 1 Vertex: (-1, -8) (green) Axis of symmetry: -1 (blue) y-intercept: (0, -3) (red)Now that we have all the information that is abovegathered, we can safely graph. The colors that arein parenthesis are the colors the dots or lines will be.Hint: The y intercept will be mirrored exactly due tothe need of symmetry.
15. 15. Problem 2 Formula: y = ax2 + bx + c y = x2 + 4x + 8 Directions: find the vertex, y-intercept and axis of symmetry. Then you may graph.
16. 16. Problem 2 Formula: y = ax2 + bx + c y = x2 + 4x + 8 First we will find the vertex’s x-coordinate using –b/2a. –b/2a = -4/2(1) = -4/2 = -2. Since -2 is our x-coordinate we will now endeavor to find our y-coordinate. y = (-2)2 + 4(-2) + 8y=4–8+8y = 4, so our vertex is at (-2, 4)
17. 17. Problem 2 Formula: y = ax2 + bx + c y = x2 + 4x + 8 Vertex: (-2, 4)Now we must find the axis of symmetry which is simplyour x coordinate, -2.
18. 18. Problem 2 Formula: y = ax2 + bx + c y = x2 + 4x + 8 Vertex: (-2, 4) Axis of symmetry: -2 We lastly need to find our y-intercept, which is (0, 8) when we follow our formula.
19. 19. Problem 2 Vertex: (-2, 4) (green) Axis of symmetry: -2 (blue) y-intercept: (0, 8) (red)