Question

What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?

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

(-1, 7)
(0, 3)
(0, 7)
(1, 9)

Answer 1

• D. (1, 9)

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Given quadratic function in the standard form and linear function in the form of a table.

Use two pairs of values in the table to determine the equation of the line.

• Let the pairs be (0, 7) and (1, 9).

The first point gives us the y-intercept, and the difference of the tow gives us the slope:

• b = 7
• m = 9 - 7 = 2

The equation of the line is:

• g(x) = mx + b
• g(x) = 2x + 7

The solution is the intersection of the graphs and it can be shown as:

• f(x) = g(x) or

• 5x² + x + 3 = 2x + 7
• 5x² - x - 4 = 0
• 5x² - 5x + 4x - 4 = 0
• 5x(x - 1) + 4((x - 1) = 0
• (x - 1)(5x + 4) = 0
• x - 1 = 0 and 5x + 4 = 0
• x = 1 and x = - 4/5

There is one of the roots, x = 1 in the answer choices so finding its y-coordinate:

• g(1) = 9 as per table so the pair is (1, 9)

The matching choice is D.