-15 points SPreCalc7 3.1.022 A quadratic function fis given. 2 fx) 2x2+32x+ 126

Question

-15 points SPreCalc7 3.1.022 A quadratic function fis given. 2 fx) 2x2+32x+ 126 (a) Express fin standard form. rx) = (b) Find the vertex and x-and y-intercepts of . (If an answer does not exist, enter DNE.) vertex x-intercepts (x,y)= (smaller x-value) (x, y) (larger x-value) y-intercept (x, y) (c) Sketch a graph of Tools 1. Select an object from the Tools menu to the lef 2. Enter coordinates in Object Properties below, or use the mouse 844 to place and move objects To enter a fractional or decimal coordinate, use Object Properties No l View our tutorial videos Object Properties Solect a Tool or Object to Bege Help (d) Find the domain and range of f. (Enter your answers using interval notation.) domain rang

Explanation / Answer

f(x)=2x2+32x+126

a. f(x)=2(x2+16x+64)+126-128

f(x)=2(x+8)2-2

b.The given equation is of the form, y=a(x-h)2+k

Where vertex(h,k)=(-8,-2)

x intercept, f(x)=0

1=(x+8)2

x+8=+-1

x=-9,-7

x intercept (-9,0),(-7,0)

y intercept, x=0

f(x)=0+0+126=126

y intercept (0,126)

Domain

There is no restriction on x

Therefore domain(-infinity,infinity)

Range

Y values cant be less than -2

So range [-2,infinity)

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