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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 x 4 x g(x) –2 1 –1 3 0 5 1 7 2 9 (-2, 10) (–1, 7) (0, 5) (1, 7)

Sagot :

The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:

g(x) = 5 + 2x.

The solution to the system of equations is found as follows:

f(x) = g(x)

2x² + x + 4 = 5 + 2x

2x² - x - 1 = 0

Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:

  • [tex]\Delta = b^2 - 4ac = (-1)^2 - 4(2)(-1) = 9[/tex]
  • [tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{9}}{4} = 1[/tex]
  • [tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{9}}{4} = -0.5[/tex]

When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).

More can be learned about a system of equations at https://brainly.com/question/24342899

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