Question

Which quadratic function is represented by the table?

Answer 1

Answer:

$\boxed{f(x)=3x^2-2x+5}$

Step-by-step explanation:

Since we know that the function of the table is a quadratic function, we can start writing this function as follows:

$f(x)=ax^2+bx+c$

Given that we have three variables $a, \ b \ and \ c$, we can solve this problem by taking three points, say:

$(0,5), \ (1,6) \ and \ (-1,10)$

So these points must satisfy the equation of the function. Therefore:

$For \ (0,5) \\ \\5=a(0)^2+b(0)+c \\ \\ 5=c \rightarrow \boxed{c=5} \\ \\ \\ For \ (1,6) \\ \\ Solving \\ \\ 6=a(1)^2+b(1)+5 \\ \\ \boxed{a+b=1} \\ \\For \ (-1,10) \\ \\Solving \\ \\10=a(-1)^2+b(-1)+5 \\ \\\boxed{a-b=5}$

So we have two equations to solve for a and b:

$(1) \ a+b=1 \ and \ (2) \ a-b=5 \\ \\ From \ 1: \\ \\ a=1-b \\ \\ From \ 2:\\ \\ a=5+b \\ \\ \\Matching: \\ \\ 1-b=5+b \ Solving: \\ \\ 1-5=b+b \\ \\ \boxed{b=-2} \\ \\ Finally: \\ \\ a=1-(-2) \therefore \boxed{a=3}$

So the quadratic function represented by the table is:

$\boxed{f(x)=3x^2-2x+5}$

Answer 2

The quadratic function which is represented by the provided table of x and f(x) is 3x^2-2x+5 in the quadratic equation form.

What is a quadratic function?

A quadratic function is the function in which the unknown variable is one and the highest power of the unknown variable is two.

The standard form of the quadratic function is,

$f(x)=ax^2+bx+c$

Here,(a,b, c) is the real numbers and (x) is the variable.

The values given in the table are,

• x       f(x)
• -2        21
• -1         10
• 0          5
• 1           6
• 2         13

Let the point (0,5) of the given table. Put these points in the above equation,

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

The value of c is 5. Put this value in the above equaiton, with point (1, 6).

$6=a(1)^2+b(1)+5\\a+b=6-5\\a+b=1$                 .....1

Now, the equation for the point (-1,10) is,

$10=a(-1)^2+b(-1)+5\\a(1)+(-1)b=10-5\\a-b=5\\a=5+b$

Put this value in the equation 1 as,

$a+b=1\\(5+b)+b=1\\2b=1-5\\b=\dfrac{-4}{2}\\b=-2$

The value of b is -2. Thus the value of a is,

$a+(-2)=1\\a=1+2\\a=3$

Put the value of a,b and c in the quadratic function,

$f(x)=3x^2-2x+5$

Thus, the quadratic function which is represented by the provided table of x and f(x) is 3x^2-2x+5 in the quadratic equation form.

Learn more about the quadratic function here;

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