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Chapter 9: Q. 348 (page 964)

f(x)=-2x2-4x-5

Short Answer

Expert verified

f(x)=-2(x+1)2-3

Step by step solution

01

Part a Step 1. Writing function in the form of f(x)=a(x-h)2+k we get,f(x)=-2(x2+2x)-5

We write the given function in the form off(x)=a(x-h)2+k

02

Part a Step 2.Using the method of completing the square, we getf(x)=-2{(x)2+2×x×1+12}-5+2f(x)=-2(x+1)2-3

Writing function in the form of f(x)=a(x-h)2+kwe get

f(x)=-2(x+1)2-3

03

Part b Step 1.Comparing the equation we get, a=-2, h=-1, k=-3the graph will open downward as the value of a is negative.

Comparing the equation withf(x)=a(x-h)2+k

04

Part b Step 2.Finding Vertex, we get(-1,-3) 

Vertex is given by(h,k)

05

Part b Step 3.Finding y intercept we get,f(0)=-2(0+1)2-3f(0)=-2-3f(0)=-5hence point is (0,-5)

finding yintercept we by puttingx=0

06

Part b Step 4.Find x intercept we get,-2x2-4x-5=0x=-(-4)±(-4)2-4(-2)(-5)2(-2)x=4±-26-4here equation has no intercept.

Find xintercept by puttingf(x)=0

07

Part b Step 5.drawing the graph we get,

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Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation.

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