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Given the quadratic equation
y = 2(x -1)^(2) + 8

Answer the following questions

"a" value =
Vertex =
Axis of Symmetry: x =
minimum or maximum (spelling counts):
Standard form = ___ x^2 - ___ x + ___

Image attached to better understand answering.

Given the quadratic equation y = 2(x -1)^(2) + 8 Answer the following questions &quot-example-1

1 Answer

5 votes

Answer:

Part 1) "a" value is
2

Part 2) The vertex is the point
(1,8)

Part 3) The equation of the axis of symmetry is
x=1

Part 4) The vertex is a minimum

Part 5) The quadratic equation in standard form is
y=2x^(2)-4x+10

Explanation:

we know that

The equation of a vertical parabola into vertex form is equal to


y=a(x-h)^(2)+k

where

(h,k) is the vertex of the parabola

if a > 0 then the parabola open upward (vertex is a minimum)

if a < 0 then the parabola open downward (vertex is a maximum)

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so


x=h

In this problem we have


y=2(x-1)^(2)+8 -----> this is the equation in vertex form of a vertical parabola

The value of
a=2

so

a>0 then the parabola open upward (vertex is a minimum)

The vertex is the point
(1,8)

so


(h,k)=(1,8)

The equation of the axis of symmetry is
x=1

The equation of a vertical parabola in standard form is equal to


y=ax^(2)+bx+c

Convert vertex form in standard form


y=2(x-1)^(2)+8


y=2(x^(2)-2x+1)+8


y=2x^(2)-4x+2+8


y=2x^(2)-4x+10

see the attached figure to better understand the problem

Given the quadratic equation y = 2(x -1)^(2) + 8 Answer the following questions &quot-example-1
User Apacay
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