MCF3M
Unit 2, Lesson 5
Finding the Vertex of a Parabola
Let 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 8 be the equation of a parabola.
Is the equation in vertex, standard, or factored form?
Find the following and use it to draw a rough sketch of what the parabola must look like.
a) The y-intercept
b) direction of opening
c) the zeroes
Is it possible to find the vertex of this graph?
What would the equation of this graph be in vertex form?
In general, we can find the vertex of a graph by:
1) Finding the x-intercepts, by setting y = 0 and solving. (usually involves factoring)
2) Add the two x-intercepts together and divide by 2 to find the x-coordinate of the vertex.
3) Substitute the x-coordinate of the vertex into the equation to find the y-coordinate.
MCF3M
Unit 2, Lesson 5
Example. Find the vertex for each of the following parabolas. Then draw a rough sketch of the parabola.
a) 𝑦 = 2𝑥 2 − 24𝑥 + 54
b) 𝑓(𝑥) = 4𝑥 2 − 1
c) 𝑦 = 4𝑥 2 − 8𝑥
Example: A diver jumps into the water from a spring board. The equation ℎ(𝑡) = −2𝑡 2 + 8𝑡 + 10 gives the height of
the diver (h), in feet, above the surface of the water after t seconds.
a) Is this equation in vertex, standard, or factored form?
b) What is the y-intercept? What does it tell you about the diver?
c) How high is the diver after 2 seconds?
d) How long is the diver in the air for?
e) Find the diver’s maximum height.
f)
Find the domain and range of this function.