Question

The graph of y = 1/2 x2 + 2x + 3 is shown. What are the solutions to the equation 1/2 x2 + 2x + 3 = x + 7?

Answer 1

Explanation:

Let's organise our information :

• the function is (1/2)x²+2x+3

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

• (1/2)x²+2x+3=x+7

• (1/2)x²+2x+3-x-7=0
• (1/2)x²+x-4=0

Now let's solve this equation :

• a= 1/2
• b= 1
• c= -4

Δ=1²-4*(1/2)*(-4)

= 9

So we have two solutions :

• 
  `\left \{ {{y=(-1-3)/(2*0.5) } \atop {x=(-1+3)/(2*0.5) }} \right.`

• y= -4
• x= 2

So the solutions are -4 and 2