Help please will mark brainliest
2 answers:
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Answer:
Purple line: 4
Red dashed line: 2
Blue line: 1/2
Step-by-step explanation:
The purple line is the steepest line, therefore it has the biggest constant of proportionality or slope. Since 4 is the biggest number among the others, we attribute it to the purple line (the one with the point C on it).
Think of it this way:
here so
The greater a is, the greater y is. So for any value of x, y will be become bigger and bigger if we increase the value of a.
Take for example this one:
Take therefore
Now take and take
therefore
When we increased this constant of proportionality, as you can see from 2 to 4, the value of y increase from 4 to 8.
Hope this is helpful. Think of it really carefully, and I'm sure you'll grasp the concept.
- Put brackets around the first two terms on the right. y = (-4x^2 - 16x) - 14
- Pull out the common factor in the first two terms. y = -4(x^2 + 4x) - 14
- Divide the middle term by 2. Add that inside the brackets. square y = -4(x^2 +4x +(4/2)^2 - 14
- y = -4(x^2 + 4x + 4) - 14 + 16 This is the step where most people stumble. The point is why is 16 added? It is because what you have done inside the brackets is multiplied 4 by - 4 (on the left). That means you have changed the equation by -16. To counter that, you must add 16 after the - 14. The result is y= -4(x^2 + 4x+4) + 2
- Express the terms inside the brackets as a square. y = - 4(x + 2)^2 + 2
B and D are both wrong. B has +4 outside the brackets. It is - 4
D is wrong because there is no 4 of any kind outside the brackets.
A is incorrectly represented inside the brackets as 16. That's not right
That only leaves C. <<<< Answer
Graphs
Notice that the red parabola and the green one are the same thing.
Red: y = -4x^2 - 16x - 14
Green: y = -4(x + 2)^2 + 2
