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ziro4ka [17]
3 years ago
15

The equation -2x2-8x = 10is rewritten in the form of -2(x-p)2+q = 0. What is the value of q?

Mathematics
1 answer:
scoundrel [369]3 years ago
4 0

Answer:

q = -2

Step-by-step explanation:

-2x²-8x = 10 (divide both sides by -2)

x² + 4x = -5 (Apply completing the square method)

x² + 4x + (4/2)²= -5 + (4/2)²

x² + 4x + 2²= -5 + 2²    (reduce left hand side using a²+2ab+b² =  (a+b)² )

(x+2)² = -5 +4

(x+2)² = -1

(x+2)² + 1 = 0   (multiply both sides by -2)

(-2)(x+2)² + 1 (-2) = 0

-2[x - (-2)]² + (-2) = 0  ---> compare this with -2(x-p)² + q = 0

We can see that p = 2 and q = -2

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You can find the constant by substituting the values given: x = 16,  f(x) = y = 2 ;

So, f(x) = y = 2  = k/16 ;

→  2 = k / 16 ;

Solve for the constant; "k" ;

Multiply EACH SIDE of the equation by "16"

→  16* (2) = (k / 16) * 16 ;

→  32 = k ;

 ↔  k = 32 ;  

As such, we can write the equation:

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Since we are given:  "x = 4" ;  Plug in that value; and solve for "y" ;

y = 32/4 = 8 .

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