1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pav-90 [236]
3 years ago
12

The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?

Mathematics
1 answer:
daser333 [38]3 years ago
4 0

Answer:

d=\frac{3}{2}=1.5

Step-by-step explanation:

We have the function:

y=a(x-2)(x-1)

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are <em>(x-2) </em>and <em>(x-1)</em>.

Therefore, our roots/zeros are <em>x=1, 2</em>.

So, the average of them are:

d=\frac{1+2}{2}=3/2=1.5

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

x=-\frac{b}{2a}

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:

x=-\frac{-3a}{2a}=\frac{3}{2}=1.5

Confirming our answer.

You might be interested in
john needed 13.71 feet of wire to fix a lamp he bought 14 half feet of wire how much did he have left ver​
motikmotik
<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Just subtract the two values:

14.5 - 13.71 = 0.79

He had 0.79 feet of wire left

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

8 0
3 years ago
Read 2 more answers
Please help me with this <br><br> 5<br> 9<br> 10<br> All real numbers
Sati [7]

i think either 5 or 9

6 0
3 years ago
Read 2 more answers
The pyramid shown has a square base that is 24 inches on each side. The slant height is 20 inches. What is the surface area of t
pashok25 [27]
The surface area for this is 1536 units.
4 0
3 years ago
Point W is on line segment VX. given VW=3 and VX=14, determine the length WX​
r-ruslan [8.4K]

Answer:11

Step-by-step explanation:14-3=11

4 0
3 years ago
Help please I'm trying to get the answer for 3 3/5 divided by 1/6
3241004551 [841]

Answer:

21 3/5

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Please help.
    9·2 answers
  • Please respond fast! Joey has a chart at his house where he records his height on his birthday each year. In a separate column,
    8·1 answer
  • How many intervals of 1/2 are between -1 and 2?
    8·1 answer
  • Factor out the greatest common factor of the expression below using the distributive property.
    5·2 answers
  • Which angle is an congruent to 3?
    13·1 answer
  • Suppose a friend is having difficulty solving -2(q-5) &gt; -3(q+1). Explain how to solve the inequality, showing all the necessa
    9·1 answer
  • $200 in the ratio 1:2:2 working out
    8·1 answer
  • Simplify the rational expression -9x/x-x^2<br><br><br>See image attatched below SOMEONE HELP ME ASAP
    6·1 answer
  • What is the value of x ?
    6·1 answer
  • Find the length of the arc.<br> 8 m<br> 315°
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!