How do I know which numbers to enter for the smaller and larger value?

Question

Fnd two x intercepts (smaller and larger x value) for the quadratic function f(x)=-x^2+2x+5

Answer 1

f(x)= - x^2 + 2x + 5 , This is a function where x intercepts may be found by setting f(x) = 0

The function can also be written as y = - x^2 + 2x + 5 and with y =0 then - x^2 + 2x + 5 = 0

This equation is a quadratic one which has two roots of x, the values of x are also the x intercepts or the values of x on the x axis when y =0. they are also the points where the parabola formed from by this equation intersects the x axis. this parabola opens down because of the negative sign of x².

The general equation of the quadratic form is ax² + bx + c = 0

- x^2 + 2x + 5 = 0, where a = -1, b = 2, and c = 5

then Δ = b² - 4ac , Δ = (2²) - 4( -1)( 5) = 4+20 = 24

x = -b ± √ Δ / 2a , x = - 2 ± √24 / 2(-1) = -2 ± 2√6/ -2 , and the two solutions are:

x = -2 + 2√6 /-2 = 1 - √ 6 , and x = -2 - 2√6 /-2 = 1 + √6

x = 3.45 , and x = -1.45 are the two roots of the equation and the two intercepts where x = 3.45 is the larger value and x = -1.45 is the smaller value. In addition, this parabola that opens down has two legs intercepting the x axis at these two points.