X-intercepts of this quadratic?

Question

I'm stuck trying to find the x-intercepts of -0.7x^2+1.1x+13, if anyone could help and show working it'd be appreciated :)

Answer 1

Let f(x ) = -0.7x² + 1.1x + 13

To find x -intercepts equate the function to 0.

-0.7x² + 1.1x + 13 = 0

Divide each side by -0.7.

-0.7x²/-0.7 + 1.1x/-0.7 + 13/-0.7 = 0/-0.7

x² -1.5714x - 18.5714 = 0

x² -1.5714x = 18.5714

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

x² -1.5714x + 0.6173 = 18.5714 + 0.6173

x² -1.5714x + 0.6173 = 19.1887

(x - 0.7857)² = 19.1887

x - 0.7857 =  ± 4.3804

Take x - 0.7857 =  + 4.3804

x = 4.3804 + 0.7857 = 5.1661.

Take x - 0.7857 =  - 4.3804

x = - 4.3804 + 0.7857 = -3.5947.

Therefore x = 5.1661 or -3.5947.