Question

For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens,and determine the y-intercept. Decide which table best illustrates these values for the equation: y= 8x^2 - 8

Answer 1

Answer: Table D

a = 8; b = 0; c = -8; parabola opens upward; y intercept at (0, -8)

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Reason:

The given equation is the same as y = 8x^2 + 0x - 8

Compare this to y = ax^2+bx+c

We see that

• a = 8
• b = 0
• c = -8

This rules out choice C because the a,b,c values don't match perfectly.

The parabola opens upward because a > 0, aka 'a' is positive. A positive 'a' value makes the parabola form a positive smile (in contrast to 'a' being negative to make a negative frown). This rules out choice A.

The y intercept always occurs when x = 0. Plug it in to get

y = 8x^2 - 8

y = 8(0)^2 - 8

y = -8

The y intercept is located at (x,y) = (0,-8). This rules out choice B.

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Summary:

We've found that

• a = 8, b = 0, c = -8
• parabola opens upward
• y intercept is at (0,-8)

All of these help us determine why choice D is the answer.