anonymous
  • anonymous
Fill in the missing term so that the quadratic equation has a graph that opens up, with a vertex of (– 2, – 16), and x intercepts at x = -6 and x = 2. (Do not include the negative sign in your answer.) y = x2 + 4x − ___
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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nirmalnema
  • nirmalnema
let us consider the blank be a so y=-16 given and x = -2 therefore -16=(-2)^2+4(-2)-a -16=4-8-a so a = 16+4 -8 =12 you can cross check by solving it....... so y = x^2+4x-12
nirmalnema
  • nirmalnema
@CeCenicole16 have u understand
anonymous
  • anonymous
Here is what you do. It is asking for a c term a c term just moves it up and down. the graph i mean. So lets plug in 0 just as a start and a reference point. x^2 + 4*x x (x+4) factored form from that it is easy to tell the roots are 0 and -4. Or you can solve for it however you want. since the midpoint from 0 to -4 is -2. That tells us the vertex is at -2. we plug -2 it into x (x+4)=-2*(-2+4)=-4 Vertex at -2,-4. Remember i said adding a c term just shifts it up and down? That means -2 will stay the same but the y will change. the vertex is at -2,-4 for now They ask for (– 2, – 16) ^ this dont matter since addinc a c term wont change it. ^ this does adding a c term will change it. we at -4 and want -16 but keep in mind y = x2 + 4x − ___ it wants it as a - Lets set up an equation for that -4-c=-16 c=12 is answer. BUt lets check x^2 + 4*x -12 we plugged in 12 for that ___ blank (-2)^2 + 4*(-2) -12 =-16 we plug in -2 IT works and below is the visual proof. https://www.google.com/search?q=x%5E2+%2B+4x+−+0&oq=x%5E2+%2B+4x+−+0&aqs=chrome..69i57j0l3.7250j0&sourceid=chrome&ie=UTF-8#q=(x)%5E2+%2B+4*(x)+-12%2C+(x)%5E2+%2B+4*(x) BTW Dont worry about the x intercept part. Cuzz just finding the vertext at -2,-16 also takes care of the wanted intercepts :)

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anonymous
  • anonymous
Also dont worry about the opening up part. SInce x2 + 4x − ___ ^ that term takes care of it opening up. not ^ c term.

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