Question

What is the quadratic function that fits the following data: (4, 9), (6, 21), (–2, –3)

Answer 1

The equation that fits into the given data is

$x^2+2x-6=0$

Quadratic Equation

This is an algebraic equation or expression that have a second degree as it highest power. An example of quadratic equation is given below

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

The given data are set of points attached to a quadratic equation and we can use it to find the quadratic equation.

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

Data;

• (4,9)
• (6,21)
• (-2,-3)

The point at (4)(9) will give us the equation

Let's substitute the value of x and y in the equation and solve

$f(4)=9\\a(4)^2+b(4)+c=9\\16a^2+4b+c-0...equation 1$

The point at(6)(21) will give the equation

Let's substitute the value of x and y in the equation and solve

$f(6)=21\\a(6)^2+b(6)+c=21\\36a+6b+c=21...equation 2$

The point at (-2)(-3) gives the equation

Let's substitute the value of x and y in the equation and solve

$f(-2)=-3\\a(-2)^2+b(-2)+c=-3\\4a-2b+c=-3...equation 3$

We have the following system of equation

$16a+4b+c=9...equation1\\36a+6b+c=21...equation2\\4a-2b+c=-3...equation3$

When we solve the above system of equation either using elimination or substitution method, we have

$a=1/2, b=1, c= -3$

substituting these values into f(x)

$(\frac{1}{2})x^2+(1) + (-3)=0\\\frac{1}{2}x^2+x-3=0$

multiply through by 2

$(2)\frac{1}{2}x^2+(2)x-(2)3=0\\x^2+2x-6=0$

The quadratic equation is $x^2+2x-6=0$

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