Algebra Exercise : Q.1 to Q.6 , Q.5 and Q.7 , Q.8 to Q.14 , Q.15 to Q.18 , Q.19 to Q. 21
( b).
The y – intercept , when x= 0
y = 02 – 4 x 0 – 12
y = 0 – 0 – 12
y = -12
(c).
Co-ordinates of vertex ; From the given equation in the book a =1 , b = -4 , c= -12
Answer 20
(a). Coordinates of center
For equation (x-a)2 + (x-b)2 = r2
The coordinates of center will be the value of constants a and b.
In the equation a = 1 and b = -1
Coordinates of center will be (1,-1)
(b). Radius = r
r2 = 20
Taking square root both side
r = √20
(c ). Area of circle = π r²
= 20 π
Answer 21
(a). The domain of any function means all the x-values for that function allowed
f(x) = -4 , take any value for x- so we can take domain as all real numbers like 1,2,3,4,5………
As there is no y-intercept given, the graph will be a horizontal line with y = 0.
(b). This is the equation of line
Domain will be any value for x of real numbers 1,2,3,4….
Let us compare this with equation of line y =mx + b
f(x) = y = -900x +100
Slope = m = – 900
y-intercept ; put x= 0 in the equation
y = -900 x 0 + 100
= 0 + 100
= 100
x –intercept; put y= 0 in the equation
0 = -900x + 100
-900x = – 100
x = -100/-900
= 1/9
( c ). The domain will be all real value for x i.e. 1,2,3,4,5………
y = 5 – (x +20)2
Open the bracket
= 5 – ( x2 + 40x + 400)
= 5 – x2 – 40x – 400
y = -x2 -40x – 395………….Equation 1
This is a quadratic equation that means graph will be a parabola.
Equation of parabola is ax2 + bx + c = 0 . If we compare with equation 1 then; a = -1 , b = -40 c = -395
As the constant ‘a’ is negative parabola will open downward.
Let us find the vertex:
x coordinate = -b/2a
= – (-40) / 2 x (-1)
= 40/-2
= -20
For y-coordinate put the value of ‘x’ in the equation 1
y = -(-20)2 – 40 x (-20) -395
= -(400) + 800 – 395
= – 400 + 800 – 395
= 5
The coordinates of vertex are ( -20 , 5 )
Line of symmetry is the center line of parabola which divides the parabola into two equal halves. It is the x-coordinate of vertex.
Hence line of symmetry x = -20
x-intercept , put y = 0 in equation 1
0= -x2 -40x – 395
a = -1 , b = -40 c = -395
Solve the equation using quadratic formula;
y – Intercept; put x = 0 in the equation 1
y = -x2 – 40x – 395
a = -1, b = -40 c = -395
y = -1 x 0 – 40 x 0 – 395
y = -395
y – Intercept will be -395
(d).
The content of square root functions are always quadratic, so easiest way is to square the equation both side
y 2 = x+2 and x+2 has to be ≥ 0
x +2 ≥ 0
x ≥ -2
So, the domain will be all real numbers ≥ -2 , i.e. -2, -1 , 1 ,2 3….
From these values of x and y if we plot the graph it will be half parabola opening to the right side.
( e )
Domain is the all real number for x i.e. 1,2,3,4,5……………..
As in the equation ‘x’ is absolute value , we have to take negative numbers also for ‘x’, to have correct solution of graph function.
Let us find the values of x and y
Now, plot the graph with above values of x and y
