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
4. Summary
In this presentation we are learning how to graph
y = ax2 + bx + c. We will graph this by first finding
the direction it opens up, the y intercept, the vertex
and the axis of symmetry. The next three slides are
devoted to how to find these.
5. How to Find the the Direction
the 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. 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. 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. How to Find the Axis of
Symmetry
y = ax2 + bx + c
The line for the axis of symmetry crosses over the
number achieved by doing the formula –b/2a.
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. 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. 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) – 3
y = 5 + - 10 – 3
y = -8, so our y coordinate is -8, making our vertex
located at (-1, -8).
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. 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. 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 above
gathered, we can safely graph. The colors that are
in parenthesis are the colors the dots or lines will be.
Hint: The y intercept will be mirrored exactly due to
the need of symmetry.
15.
16. 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.
17. 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) + 8
y=4–8+8
y = 4, so our vertex is at (-2, 4)
18. Problem 2
Formula: y = ax2 + bx + c
y = x2 + 4x + 8
Vertex: (-2, 4)
Now we must find the axis of symmetry which is simply
our x coordinate, -2.
19. 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.
20. Problem 2
Vertex: (-2, 4) (green)
Axis of symmetry: -2 (blue)
y-intercept: (0, 8) (red)
