Download - Tutorial 1 Quadratics n
CHAPTER ONE: QUADRATICS
Tutorial 1
1. Multiply out the following expressions and collect like terms.
a. (a+2)(a+3)
b. (c−4)(c−2)
c. (e+6)(e−1)
d. (h+5 )2
Answer: a. a2+5 a+6 b. c2−6 c+8 c.
e2+5e-6 d. h+10h+25
2. Factorise the following quadratic expressions.
a. x2+6 x+8
b. y2+9 y+20
c. a2−9
d. r2−2r−15
e. ( x+3 )2−9
f. 2 x2+5 x+2
g. 2 x2+14 x+24
h. 9 x2−6 x+1
Answer: a. ( x+2 ) (x+4 ) b. ( y+4 ) ( y+5 ) c. (r−5 ) (r+3 ) d. (a+3 ) (a−3 ) e. x (x+6 )
f. (2 x+1 ) ( x+2 ) g. 2 ( x+3 ) ( x+4 ) h.
(3 x−1 )2
3. Solve the following equations.
a. x2−11 x+24=0
b. x2−64=0
c. 3 x2−5 x+2=0
d. 9 x2−12 x+4=0
e. x2−x=20
f. x−1=6x
Answer: a. x=8 or x=3 b. x=−8 or x=8
c. x=2/3 or x=1 d. x=23
(repeated)
e. x=−5 or x=4 f. x=−2 or x=3
4. Write the following in completed square form.
a. 2 x2+4 x+6
b. −1 x2−2x+5
c. 5 x2−10 x+7
d. −3 x2−12x
Answer: a. 2 ( x+1 )2+4 b. −( x+1 )2+6 c.
5 ( x−1 )2+2 d. −3 ( x+2 )2+12
5. Use the quadratic formula to solve the following equations, where possible.
a. x2+8 x+5=0
b. x2−5 x−19=0
c. 3 x2+2x−4=0
d. x2−12=0
Answer: a. x=−0.683 or x=−7.317b. x=7.525 or x=−2.525c. x=0.869 or x=−1.535d. x=3.464 or x=−3.464
6. Find the value of discriminant and use it to find the number of real roots for each of the following equations.
a. x2−3 x+4=0
b. 4 x2−3x=0
c. 3 x2+4 x+1=0
d. x2+10x+25=0
Answer: a. -7, no real roots b. 9, two real rootsc. 4, two real roots d. 0, one repeated root
7. Sketch the quadratic curve.
a. y=x2+4 x+9
b. y=x2+4 x+3
c. y=x2+6 x−1
d. y=x2+x+2
e. y=x2+ 12x+1
Answer: a. ( x+2 )2+5; x = -2; (-2, 5) intercept-y (0, 9)
b. ( x+2 )2−1; x = -2; (-2, -1) intercept-y (0, 3)
c. ( x+3 )2−10; x = -3; (-3, -10) intercept-y (0, -1)
d. (x+ 12 )
2
+ 74
; x = −12
; (−12
, 74
) intercept-y (0,
2)
e. (x−14 )
2
+ 1516
; x = 14
; (14
, 1516
) intercept-y (0, 1)