# Quadratic Functions and the Substitution Method (Math Problem Sample)

1:FIND THE VALUE OF A, B,C. WHERE a=b-1 and=b+1 and b=b

2:. Draw the graph of y=x^2+x-3 for -3≤x≤2

3: SOLVE THE SIMULTANEOUS EQUATIONS

3x2-5xy+2y2=33

4x-3y=14

Mathematic Assignment 0004

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Question 1 Answer

Let the sides of the triangle be a,b,c

a=b-1 and=b+1 and b=b

r=△s=ss-as-bs-cs=4

s=3b2

b2+1b2b2-13b2=4

Square both side

b2+1b2b2-13b2=16

Simplify the equation

b+22b2b-223b2

(b2-4)b=192b

Which implies that b3-4b=192b

Which implies that b3=196b

Divide both side by b ,

b2=196 which implies that b=14

Then a=13 ,b=14 ,c=15

Question 2 Answer

Rewrite the equation x2+x-3=0 as quadratic function y=x2+x-3 . Draw the graph of y=x2+x-3 for -3≤x≤2

x

-3

-2

-1

0

1

2

y

3

-1

-3

-3

-1

3

The solution for the equation y=x2+x-3 can be obtained by looking at the points where the graph y=x2+x-3 cuts the x-axis.

The graphy=x2+x-3, cuts they -axis at x 1.3 and x –2.3

So, the solution for the equation x2+x-3 is x 1.3 or x –2.3.

Question 3 Answer

Solve the simultaneous equation by substitution method.

Get the values of y. Then, the values of x.

3x2-5xy+2y2=33………. i

4x-3y=14……………. ii

Make x to be the subject of the formular using equation (ii)

x=14+3y4

Substitute x to equation (i) above.

3(14+3y4)-5(14+3y4)y+2y2=33

Multiply both sides by 4

42+9y-70-15y+8y2=165

After substituting, the equation becomes

8y2-6y-193

Find the value of y using quadratic formula.

y=6±62+4×8×1932×8

It follows that y is eq

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