Question: Algebraic methods 2. a) Express x2 + 4x - 7 in the form (x + p)2 - q, where p and q are integers. x

Algebraic methods 2. a) Express x2 + 4x - 7 in the form (x + p)2 - q, where p and q are integers. x 2+ 4x - 7 ( x + 4/2 ) ? = (x+2)2 , 2 2 = 4 ( x + 2 ) - + 4 constant difference between - 7 and +4 is 11 So x 2 + 4x - 7 = (x+ 2) 2 - 11 b) Hence, or otherwise, find the coordinates of the minimum point of the curve y = x2 + 4x - 7. X = 2X1 = - 2 y = (-2) 7+ 4(-2) - 7 = 4+ (-8)-7 Thegone, the coordinates of = - 11 the minimum point are ( - 2 , - 1 1 ) c) Solve the equation for x and sketch a graph to show the root/s of the equation. X + 1 =3/4 X + 4 X Page 2 Version

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

please answer the questions that are circled. 2. Solve (x + 3)- Skill Building In Problems 5-32, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded...

calculate the dividend/cash flow each year using thr growth rate. determine where the growth if the company becomes constant (this is the key constant growth rate model), this is called the terminal...

Write the function as a composition of two functions. 1 2 y: (x2+4x) 7 7(x2+4x)T +2 Choose the correct answer below. 1 If f(X) =x7 7x7 + 2 and g(x) =x2 +4x, then y=f[g(x)]. i 2 V If f(x) = x2 + 4x...

Which ordered pairs are solutions to the following system of equations? 3x + y = 5 5x - 4y = -3 A. (1, 2) B. (2, -1) C. (1, 2) and (2, -1) D. None of the above Which system of equations represents...

Problem 6: Battleship Blueprint class for Ship objects 10 points total; pair-optional This is one of only two problems in this assignment that you may complete with a partner. See the rules for...

1. [-/1 Points] DETAILS LARCALCET7 4.1.008.MI. Find the value of the derivative (if it exists) at the indicated extremum, (If an answer does not exist, enter DNE.) -2, 10v3 (x) = - 5xVx + 1 F (=2) =...

Rules of the game In our version of Battleship, each player has an 8 x 8 board containing a collection of five ships: one battleship, of length 4 one cruiser, of length 3 one tanker, of length 3 two...

1. Factor the following polynomial completely: f(x) = x4 -5x2 -14 A. f (x) = (x - V7)(x +v7)(x - v2)(x+ v2) B. f (x) = (x - V7i) (x+ V7i)(x - v2)(x+ v2) C. f ( x) = (x - V7) (x + v7)(x - VZi)(x+ v2i)...

d 7. Given the function f(x) =x2 -5, determine the value of f( f (-1)). A. -8 B. -4 C. 11 D. 16 Use the following information to answer the next question An orchestra has 2 violinists, 3 cellists,...

On January 1, 2015, Parula Corporation owned 90% of the 14,400 outstanding shares of Sope Inc. Parula accounts for its investment using the equity method. On January 1, 2015, Sope had shareholders'...

Roughly 4% of American women have had breast augmentation surgery (300,000 per year, compared to 40,000 breast reduction surgeries in women, and 20,000 breast reduction surgeries in men per year)...

You have the following information: Sales = $ 3 , 9 5 0 Net Profit Margin = 6 % Total Assets = $ 3 , 6 5 0 Liabilities to Assets Ratio = 4 2 % . What is the ROE? Group of answer choices 5 , 6 4 % 6 ....

A shaft of diameter 3.75 cm is rotating in a fixed housing of diameter D=3.95 cm. It is lubricated by an oil with a viscosity of = 0.40 Ns/m 2 The shaft is rotating with an electric motor with...