1. Work with the quadratic function y(x) = 2x² + 2x + 2. (a) Find the roots. (b) Define the axis of symmetry and calculate its value. (c) Does the function have a maximum or a minimum? Why? (d) What is the value of the function at the maximum (or minimum)? (e) Graph the function.

1. Work with the quadratic function y(x) = 2x² + 2x + 2. (a) Find the roots. (b) Define the axis of symmetry and calculate its value. (c) Does the function have a maximum or a minimum? Why? (d) What is the value of the function at the maximum (or minimum)? (e) Graph the function.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section9.2: Transformations Of Quadratic Functions

Problem 50PFA

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Question

can you please explain the answer by solving this question again?

1. Work with the quadratic function y(x) = 2x² + 2x + 2.
(a) Find the roots.
(b) Define the axis of symmetry and calculate its value.
(c) Does the function have a maximum or a minimum? Why?
(d) What is the value of the function at the maximum (or minimum)?
(e) Graph the function.
0 @ 1 = - 12/2
2.
-√√-3 r₂ = -2 +15=3
2
2
(D
(b) The axis of symmetry is the line about which
y(x) is symmetric. x* =
1₁+√₂ = 1/2
Ⓒ
(c) The function has a minimum at x =-½/2
because aso
y (-2) = ²/3 - ²/2 +2
2
Ⓒ (d)
(e)
- ½/22
1
दू
In yo
O
VIT
= 6
x

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Follow-up Questions

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Follow-up Question

where did you get the 1/4's from in the highlighted part?

So
given
ac
y
y
y = 2x² +2x+2
So
at
(1
=
= 2 (x² + x) + 2
2
X
(8 + 3) =
2)
2(x²+x+/4/4/4
- 4 - 4)
2
y = 2 ( x + 1)² - 3/2
funtion
2
( x + ¹)² = ² ( + ₁) +
-
This
parabola
²(x + 2) ²
2
is a
has
+2.
upw and
+2
minimum
parabola.

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