Vertex Form

Multiple Choice

What is the significance of the vertex of a quadratic function?

• It determines the direction of the parabola.

• It represents the highest or lowest point of the parabola.

• It gives the x-intercepts of the parabola.

• It shows the axis of symmetry.

​Together

Fill in the Blanks

Without looking at your calculator, what do you think the vertex of k(x) would be if its equation is k(x)=(x+5)²-7?

Multiple Choice

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

• (5, -4)
• (-5, -4)
• (-15, -4)
• (15, -4)

Multiple Choice

Which equation has a vertex of (-3, 4)?

• y = 2(x+3)² + 4
• y = (x+3)² - 4
• y = (x-3)² + 4
• y = 2(x - 3)² + 4

Multiple Choice

4. Practice. Write a quadratic function in vertex form to make each of the following vertices.

   I. Vertex = (2,-11)

• k(x)=(x+2)² -11

• k(x)=(x-2)² -11

• k(x)=(x-2)² +11

• k(x)=(x+2)² +11

Multiple Choice

4. Practice. Write a quadratic function in vertex form to make each of the following vertices.

   II. Vertex = (-18,7)

• j(x)=(x+18)² +7

• j(x)=(x-18)² +7

• j(x)=(x+18)² -7

• j(x)=(x-18)² -7

Open Ended

Compare the standard form and vertex form of a quadratic function. What do they have in common, and how are they different?

Multiple Choice

Identify the a, h, and k terms in the following equation: $$\left(x+4\right)^2-3$$  

• a=-1, h=4, k=3

• a=-1, h=-4, k=3

• a=1, h=4, k=3

• a=1, h=-4, k=-3

Multiple Choice

What is the vertex of the parabola: y=2(x-3)²+4

• (3,4)
• (-3,4)
• (3, -4)
• (-3,-4)

Multiple Choice

What is the equation of this graph?

• f(x) = (x -5)² + 1
• f(x) = (x - 1)² - 5
• f(x) = (x + 1)² - 5
• f(x) = (x + 5)² +1

Multiple Choice

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1
• f(x) = (x + 2)² - 1
• f(x) = -(x + 2)² - 1
• f(x) = -(x - 2)² - 1

Open Ended

Do you have any questions about vertex form or would you like to know more about how transformations affect quadratic functions?