How do you solve the simultaneous equations ?
y = x + 4
y = 2x² + 3x - 1

(1.16, 5.16) and (-2.16, 1.84)    to the nearest hundredth.

Step-by-step explanation:

By substitution. You substitute y = x + 4 into the second equation:

x + 4 = 2x^2 + 3x - 1

2x^2 + 2x - 5 = 0

x = [ -2 +/- sqrt (2^2 - 4*1*-5) ] / 2*2

= -1/2 +/1 sqrt 24/4

= 1.158 , - 2.158

When x =  1.158 , y = 1.158 + 4 = 5.158

When x = -2.158, y = -2.158 + 4 = 1.842.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this