Question

Given: f(x)= x² + 3x-4 and g(x) = x-4​

Answer 1

x-intercept of f(x)=x²+3x-4 is (1,0) &(-4,0)

x-intercept of g(x)=x-4 is (4,0)

y-intercept of f(x)=x²+3x-4 is (0,-4)

y-intercept of g(x)=x-4 is (0,-4)

Explanation:

`f(x) = x {}^(2) + 3x - 4 \\ to \: find \: x \: intercept \: subistitute \: f(x) = 0 \\ 0 = x {}^(2) - 3x - 10 \\ x { }^(2) - 3x - 1 = 0 \\ x {}^(2) + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5 \\ the \:equation \: x \: intercept \: are \: - 2and \: 5 \\ f(0) = 0 {}^(2) + 3(0) - 4 \\ - 4 \: is \: y \: intercept \: of \: f(x) = x {}^(2) + 3x - 4 \\ where \: as \: for \: g(x) = x - 4 \\ to \: find \: x \: intercept \: f(x) = 0 \\ 0 = x - 4 \\ - x = - 4 \\ x = 4 \\ 4is \: the \: x \: intercept \: and \: for \: the \: y \: intercept \\ g(0) = 0 - 4 \\ y = - 4is \: the \: y \: intercept.`