Identifying the Vertex of Quadratic Functions

This lesson covers the vertex form of quadratic functions, exploring its significance and applications. It begins with an introduction to various forms of quadratic functions, including standard and factored forms. The lesson then delves into identifying graphical features such as zeros and the axis of symmetry. The vertex form is highlighted for its ability to easily show the turning point of a parabola. The lesson also demonstrates how to use vertex form to model real-world scenarios, emphasizing transformations like shifts and compressions. The session concludes with a summary of key concepts.

What is the main focus of Unit 10 Lesson 7?

• Solving linear equations

• Vertex form of a quadratic function

• Factoring polynomials

• Graphing linear functions

What is the leading coefficient of the quadratic function f(x) = x^2 - 6x + 8?

• 6

• 8

• 1

• 0

In the factored form of f(x) = x^2 - 6x + 8, what are the zeros of the function?

• x = -6 and x = 8

• x = 0 and x = 8

• x = 2 and x = 4

• x = -2 and x = -4

How do you find the axis of symmetry for the quadratic function f(x) = x^2 - 6x + 8?

• By setting the function equal to zero

• By graphing the function

• By finding the y-intercept

• Using the formula x = -b/2a

What is the turning point of the function g(x) = (x - 6)^2 - 4?

• (-6, 4)

• (6, 4)

• (6, -4)

• (0, -4)

How is the function h(x) = (x + 2)^2 + 1 shifted from the parent function y = x^2?

• 2 units right and 1 unit down

• 2 units left and 1 unit down

• 2 units left and 1 unit up

• 2 units right and 1 unit up

What is the vertex of the function y = 5(x - 4)^2 + 20?

• (4, 5)

• (5, 20)

• (4, 20)

• (0, 20)

What is the value of 'a' in the function y = a(x - 10)^2 + 12 if the point (0, 8) lies on the function?

• -0.04

• 0.04

• 4

• -4

Why is the leading coefficient negative in the function modeling the domed roof?

• Because the function is linear

• Because the parabola opens downwards

• Because the vertex is at the origin

• Because the parabola opens upwards

What is the final formula for the domed roof function?

• y = -0.04(x - 10)^2 + 12

• y = 0.04(x - 10)^2 + 12

• y = -0.04(x + 10)^2 + 12

• y = 0.04(x + 10)^2 - 12