Question

50 POINTS PLEASE HELP show work answer all 3

Answer 1

Answer:

b.) The graph's x-intercepts are similar to ½(x - 5)(x + 2).

a.) [-2, 0], [5, 0]

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b.) The graph has a maximum value because the graph opens down [-2 = A].

a.) [-3, -4]

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d) [0, -5]

c) -2 = x

b) [-2, -9] → [h, k]

a) -1, 5 = x

Explanation:

b) Both graphs have the binomial of [x - 5][x + 2], so the x-intercepts never altered.

a) Set the binomial equal to zero, and you will get your x-intercepts of [-2, 0] and [5, 0].

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b) When A is negative, your graph will have a maximum value [opens down], whereas when A is positive, your graph will have a minimum value [opens up].

a) According to the Vertex Formula, y = A[X - H]² + K, [H, K] represents the vertex, plus, -H gives you the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL labeling your vertex. Additionally, K gives you the NORMAL TERMS.

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d) The y-intercept is your C-term, so in this case, it is [0, -5].

c) To find the axis of symmetry, use this formula:

$\frac{-b}{2a} = x$

Whatever the opposite of your B-term is, you take that and divide it by twice your A-term.

b) To find the vertex, in this case, you have to go from Standard Form to Vertex Form by completing the square, using this formula to get part of your new C-term:

$[\frac{b}{2}]^{2}$

When done, you get this:

$y = {x}^{2} + 4x + 4 \\ \\ y = [x + 2]^{2}$

Then, you have to deduct some number from 4 that gave you -5 in the first place, and that integer is -9. So, here is the result:

$y = [x + 2]^{2} - 9$

From here, we can see that our vertex is [-2, -9].

a) When the binomial is set to equal to zero, you get this:

${x}^{2} + 4x - 5 \\ \\ [x - 1][x + 5] = 0 \\ \\ 1, \: -5 = x$

e) See above photograph

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