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wariber [46]
3 years ago
15

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?

Mathematics
1 answer:
kirill [66]3 years ago
3 0

Answer:

Step-by-step 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=\frac{-1-3}{2*0.5} } \atop {x=\frac{-1+3}{2*0.5} }} \right.
  • y= -4
  • x= 2

So the solutions are -4 and 2

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Answer:

\large \boxed{\sf \ \ 69 \ \textbf{touchdowns } 11 \ \textbf{field goals } \ }

Step-by-step explanation:

Hello,

Touchdown is 7 points, field goals is 3 points

Let's note a the number of touchdowns and b the number of field goals, we can write

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<=> 7a + 3b -3a - 3b = 516 - 240 = 276

<=> 4a = 276

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And then from (1) b = 80 - 69 = 11

Hope this helps

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