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To find the coordinates for the function ( g(h) = -6h^2 - 2h + h ) with the given inputs, we need to evaluate the function at each input value. Let’s calculate:

For ( h = -8 ):
g(−8)=−6(−8)2−2(−8)+(−8)
g(−8)=−6(64)+16−8
g(−8)=−384+16−8
g(−8)=−376
So, the coordinate is ((-8, -376)).

For ( h = -6 ):
g(−6)=−6(−6)2−2(−6)+(−6)
g(−6)=−6(36)+12−6
g(−6)=−216+12−6
g(−6)=−210
So, the coordinate is ((-6, -210)).

For ( h = -4 ):
g(−4)=−6(−4)2−2(−4)+(−4)
g(−4)=−6(16)+8−4
g(−4)=−96+8−4
g(−4)=−92
So, the coordinate is ((-4, -92)).

For ( h = -2 ):
g(−2)=−6(−2)2−2(−2)+(−2)
g(−2)=−6(4)+4−2
g(−2)=−24+4−2
g(−2)=−22
So, the coordinate is ((-2, -22)).

For ( h = 0 ):
g(0)=−6(0)2−2(0)+0
g(0)=0
So, the coordinate is ((0, 0)).

Therefore, the coordinates for the function ( g(h) = -6h^2 - 2h + h ) with the inputs (-8, -6, -4, -2, \text{and } 0) are:

((-8, -376))
((-6, -210))
((-4, -92))
((-2, -22))
((0, 0))
make this like a 9th grader wrote it

1 answer

Sure! Here’s a simpler version of your calculations that sounds like a 9th grader wrote it:

To find the coordinates for the function \( g(h) = -6h^2 - 2h + h \), I need to plug in some values for \( h \) and calculate the results. Let's do that for \( h = -8, -6, -4, -2, \) and \( 0 \).

  1. For \( h = -8 \): \[ g(-8) = -6(-8)^2 - 2(-8) + (-8) \] First, calculate \((-8)^2\): \[ g(-8) = -6(64) + 16 - 8 \] Now, multiply: \[ g(-8) = -384 + 16 - 8 \] Then, add them up: \[ g(-8) = -384 + 8 = -376 \] So, the coordinate is (-8, -376).

  2. For \( h = -6 \): \[ g(-6) = -6(-6)^2 - 2(-6) + (-6) \] Calculate \((-6)^2\): \[ g(-6) = -6(36) + 12 - 6 \] Now, multiply: \[ g(-6) = -216 + 12 - 6 \] Add them: \[ g(-6) = -216 + 6 = -210 \] So, the coordinate is (-6, -210).

  3. For \( h = -4 \): \[ g(-4) = -6(-4)^2 - 2(-4) + (-4) \] Calculate \((-4)^2\): \[ g(-4) = -6(16) + 8 - 4 \] Now, multiply: \[ g(-4) = -96 + 8 - 4 \] Add them: \[ g(-4) = -96 + 4 = -92 \] So, the coordinate is (-4, -92).

  4. For \( h = -2 \): \[ g(-2) = -6(-2)^2 - 2(-2) + (-2) \] Calculate \((-2)^2\): \[ g(-2) = -6(4) + 4 - 2 \] Now, multiply: \[ g(-2) = -24 + 4 - 2 \] Add them: \[ g(-2) = -24 + 2 = -22 \] So, the coordinate is (-2, -22).

  5. For \( h = 0 \): \[ g(0) = -6(0)^2 - 2(0) + 0 \] Since everything is multiplied by 0: \[ g(0) = 0 \] So, the coordinate is (0, 0).

Therefore, the coordinates for the function \( g(h) \) with the inputs \( -8, -6, -4, -2, \) and \( 0 \) are:

  • (-8, -376)
  • (-6, -210)
  • (-4, -92)
  • (-2, -22)
  • (0, 0)

That's it!