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Algebra 1 - vertex, axis of symmetry, domain, and range











































Part 1 − Find the vertex, axis of symmetry, domain, and range of the graph of y = −2x2 − 6x + 1. Show all work for full credit.

Part 2 − Using complete sentences, explain how you can determine the axis of symmetry, the domain, and range without graphing y = −2x2 − 6x + 1.

Comments for Algebra 1 - vertex, axis of symmetry, domain, and range

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Jun 24, 2012
vertex, axis of symmetry, domain, and range
by: Staff


The answer:

Part 1 − Find the vertex, axis of symmetry, domain, and range of the graph


y = -2x² - 6x + 1



Using the quadratic formula is probably the fastest way:

ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/(2a)

a = -2

b = -6

c = 1



The x value of the vertex is the first part for the solution for x

x value of Vertex = -b/(2a)

x value of Vertex = -(-6)/[2*(-2)]

x value of Vertex = 6/[2*(-2)]

x value of Vertex = 3/(-2)

x value of Vertex = -3/2

x value of Vertex = -1.5



The y value of the vertex

y = -2x² - 6x + 1

y = -2*(-3/2)² - 6*(-3/2) + 1

y = -2*(9/4) - 6*(-3/2) + 1

y = -9/2 + 9 + 1

y = -9/2 + 10

y = 10 - 9/2

y = 20/2 - 9/2

y = (20 - 9)/2

y = 11/2

y = 5.5


vertex = (-1.5, 5.5)

axis of symmetry:

x = -1.5



>>> the final answer is:

Vertex = (-1.5, 5.5)


Axis of Symmetry: x = -1.5


Domain of the function

-∞ < x < ∞


Range of the function

y ≤ 5.5



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http://www.solving-math-problems.com/images/parabola-vertex-axis-of-symmetry-2012-06-24.png







Part 2 − Using complete sentences, explain how you can determine the axis of symmetry, the domain, and range without graphing y = -2x² - 6x + 1



Axis of Symmetry: The Axis of Symmetry is the vertical line passing through the vertex. Since the vertex is (-1.5, 5.5), the Axis of Symmetry is x = -1.5.

Domain: The Domain is all possible values of x. x can be any real number which can be used in the function. -∞ < x < ∞


Domain: The Range is all possible values of y. y can be any real number equal to or less than the value of y at the vertex. y ≤ 5.5





Thanks for writing.

Staff
www.solving-math-problems.com


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