Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

12. The table of values below describes a quadratic relation. Find the missing value and include calculations that demonstrate that this is the correct value.

12 The Table Of Values Below Describes A Quadratic Relation Find The Missing Value And Include Calculations That Demonstrate That This Is The Correct Value class=

Sagot :

Answer:

The quadratic equation is;

y = 3x^2-7x + 5

when x = 4, y = 25

Step-by-step explanation:

Mathematically, the general form of a quadratic equation is;

y = ax^2 + bx + c

From the first point, we have that x = 0

Thus;

5 = a(0)^2 + b(0) +c

c = 5

Now, in a case when x is 2

3 = a(2)^2 + b(2) + 5

3 = 4a + 2b + 5

4a + 2b = -2 ••••••(i)

when x = 6

71 = a(6)^2 + b(6) + 5

66 = 36a + 6b ••••••(ii)

From equation i,

2b = -2-4a ••••(iii)

we can rewrite equation ii as

66 = 36a + 3(2b)

Substitute iii into ii

66 = 36a + 3(-2-4a)

66 = 36a - 6 - 12a

66 + 6 = 36a -12a

24a = 72

a = 72/24

a = 3

Recall;

2b = -2-4a

2b = -2-4(3)

2b = -2-12

2b = -14

b = -14/2

b = -7

So the quadratic equation would be;

y = 3x^2 -7x + 5

Now let us test;

when x = 10, y = 235

That would be:

y = 3(10)^2 -7(10) + 5

y = 300 - 70 + 5

y = 235

This shows that the derived quadratic equation is correct

Now, when x = 4; we have it that;

y = 3(4)^2 -7(4) + 5

y = 48 -28 + 5

y = 20 + 5 = 25

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.