About Vertex Form of a Parabola:
The vertex of a parabola is the lowest point for an upward-facing parabola or the highest point for a downward-facing parabola. When working with parabolas of the form: f(x) = ax2 + bx + c, we can find the vertex by completing the square and obtaining the vertex form or from the vertex formula. When we complete the square, we are able to change the form to: f(x) = a(x - h)2 + k, where the vertex is given as: (h, k). Alternatively, we can just find the vertex as: (-b/2a, f(-b/2a)).
Test Objectives
- Demonstrate the ability to write a quadratic equation in vertex form
- Demonstrate the ability to find the vertex for a parabola
#1:
Instructions: Find the vertex form and state the vertex.
$$a)\hspace{.2em}f(x)=3x^2 - 24x + 38$$
$$b)\hspace{.2em}f(x)=x^2 - 18x + 91$$
Watch the Step by Step Video Lesson View the Written Solution
#2:
Instructions: Find the vertex form and state the vertex.
$$a)\hspace{.2em}f(x)=2x^2 - 8x + 10$$
$$b)\hspace{.2em}f(x)=-x^2 + 4x + 4$$
Watch the Step by Step Video Lesson View the Written Solution
#3:
Instructions: Find the vertex form and state the vertex.
$$a)\hspace{.2em}f(x)=\frac{1}{3}x^2 - 4x + 21$$
$$b)\hspace{.2em}f(x)=-18x^2 - 144x - 279$$
Watch the Step by Step Video Lesson View the Written Solution
#4:
Instructions: Find the vertex form and state the vertex.
$$a)\hspace{.2em}f(x)=-2x^2 + 9$$
$$b)\hspace{.2em}f(x)=-\frac{1}{3}x^2 + 6x - 32$$
Watch the Step by Step Video Lesson View the Written Solution
#5:
Instructions: Find the vertex form and state the vertex.
$$a)\hspace{.2em}f(x)=10x^2 + 6$$
$$b)\hspace{.2em}f(x)=-8x^2 + 80x - 194$$
Watch the Step by Step Video Lesson View the Written Solution
Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}f(x)=3(x - 4)^2 - 10$$ $$\text{Vertex:}\hspace{.25em}(4, -10)$$
$$b)\hspace{.2em}f(x)=(x - 9)^2 + 10$$ $$\text{Vertex:}\hspace{.25em}(9, 10)$$
Watch the Step by Step Video Lesson
#2:
Solutions:
$$a)\hspace{.2em}f(x)=2(x - 2)^2 + 2$$ $$\text{Vertex:}\hspace{.25em}(2, 2)$$
$$b)\hspace{.2em}f(x)=-(x - 2)^2 + 8$$ $$\text{Vertex:}\hspace{.25em}(2, 8)$$
Watch the Step by Step Video Lesson
#3:
Solutions:
$$a)\hspace{.2em}f(x)=\frac{1}{3}(x - 6)^2 + 9$$ $$\text{Vertex:}\hspace{.25em}(6, 9)$$
$$b)\hspace{.2em}f(x)=-18(x + 4)^2 + 9$$ $$\text{Vertex:}\hspace{.25em}(-4, 9)$$
Watch the Step by Step Video Lesson
#4:
Solutions:
$$a)\hspace{.2em}f(x)=-2x^2 + 9$$ $$\text{Vertex:}\hspace{.25em}(0, 9)$$
$$b)\hspace{.2em}f(x)=-\frac{1}{3}(x - 9)^2 - 5$$ $$\text{Vertex:}\hspace{.25em}(9, -5)$$
Watch the Step by Step Video Lesson
#5:
Solutions:
$$a)\hspace{.2em}f(x)=10x^2 + 6$$ $$\text{Vertex:}\hspace{.25em}(0, 6)$$
$$b)\hspace{.2em}f(x)=-8(x - 5)^2 + 6$$ $$\text{Vertex:}\hspace{.25em}(5, 6)$$
