MAT 095 Lecture Notes - Lecture 28: Quadratic Formula, Discriminant, Quadratic Equation

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plummoose320

20 Dec 2016

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Provide a generalization to each of the terms listed in this section. Quadratic equation: this is the formula for the quadratic equation: ax2 + bx + c = 0. 4 4 ( 3) y = y = y = Quadratic formula: this is the formula for the quadratic formula: x = b b2 4ac. Quadratic formula derivation ax2 + bx + c = 0 ax2. 0 a a bx a c x2 + b a x + = 0 a c a c a x2 + b a x2 + b a x + b c c a x + x + a b2. = 0 c c a b2. 2a x2 + b a (cid:18)x + (cid:18)x + s(cid:18)x + x + x + 2a x = b b2 4ac. 6y + 3 = 4y2 (6y + 3) (6y + 3) = 4y2 (6y + 3) 4 y = y = y = y =

Related Questions

(A)Section 1.2 talks about modeling with equations. Our everyday livesare filled with models and applications of mathematics. Give anexample where you had to APPLY a formula or math principles tosolve a situation in real life. Such as using a formula or workingout an equation. Describe the problem and work it out

Section 1.3 talks about modeling with quadratic equations.Create a unique, real-world word problem that models either, (1)the area of a rectangle, (2) distance, speed, & time, or (3)the path of a projectile.

Describe your problem and work out the quadratic equation youfind

EXE

(B) An equationinvolving a rational power is given. Find all solutions of theequation 1-10.

1. x^3/ 2 =27 2.x^2/3 = 4

3. x^2/5 ?16 =0 4.x^5/ 2 + 32 = 0

5.32x^5/3 +1 =0 6.64x^3/ 4 ?125 = 0

7. (x? 2)^1/5 =?2 8.(2x ?3)^2/3 = 4

9. 5(x+3)^2/3 -45=0 10.(x-3)^3/4 +1/8 = 0

(C)Section 2.4 dealswith lines and slopes. Give an example where the concept of slopeis used in real life. Describe the increase/decrease in the contextof the example and why it is important in the real world.

(D )Section 3.2 dealswith lines and slopes. Give an example where the concept of slopeis used in real life. Describe the increase/decrease in the contextof the example and why it is important in the realworld

magentacoyote308

Can someone please help me with this? I don't even think the ones I answered are correct.

15. Solve the equation by using the quadratic formula. (Enteryour answers as a comma-separated list.)

x² ? 4x ? 4 = 0

(a) Give exact real answers.
x =
(b) Give answers rounded to two decimal places.
x =

16. Use any method to find the exact real solution, if itexists. (Enter your answers as a comma-separated list. If there isno solution, enter NO SOLUTION.)

(w^2/6) - (w/3) - 4 =0

17. Solve using quadratic methods. (Enter your answers as acomma-separated list.)

(x + 5)² + 5(x + 5) + 4 = 0

x =

18. Consider the following equation.

y = (-1/22)x^2 +x

(a) Find the vertex of the graph of the equation.
(x , y) = ( )
(b) Determine if the vertex is a maximum or minimum point.

(c) Determine what value of x gives the optimal valueof the function.
x =

(d) Determine the optimal (maximum or minimum) value of thefunction.
y =

20. The daily profit from the sale of a product is given byP = 14x ? 0.1x² ? 50 dollars,where x is the number of units of production.

(a) What level of production maximizes profit?
units

(b) What is the maximum possible profit?
$

21. If the supply function for a commodity is p =q² + 14q + 49 and the demand functionis p = â11q² + 92q + 469,find the equilibrium quantity and equilibrium price.
(q, p) = ( )

22. The supply and demand for a product are given by 2p? q = 80 and pq = 100 + 35q,respectively. Find the market equilibrium point.
(q, p) = ( )

23. The total costs and total revenues for a company arerepresented by the equations shown below, where xrepresents the number of production units. Find the break-evenpoints. (Enter your answers as a comma-separated list.)

C(x) = 2100 + 20x +x²
R(x) = 120x

x = units

24. If, in a monopoly market, the demand for a product isp = 130 ? 0.40x and the revenue function isR = px, where x is the number of unitssold, what price will maximize revenue? (Round your answer to thenearest cent.)
$

28.