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2 answers:
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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 = <em>A</em>].
a.) [-3, -4]
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d) [0, -5]
c) -2 = x
b) [-2, -9] → [<em>h</em>, <em>k</em>]
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 <em>A</em> is negative, your graph will have a <em>maximum value</em> [<em>opens down</em>], whereas when <em>A</em> is positive, your graph will have a <em>minimum value</em> [<em>opens up</em>].
a) According to the <em>Vertex Formula</em>, <em>y = A</em>[<em>X - H</em>]<em>² + K</em>, [<em>H</em>, <em>K</em>] 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 <em>y-intercept</em> is your C-term, so in this case, it is [0, -5].
c) To find the <em>axis of symmetry</em>, use this formula:
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 <em>Standard Form</em> to <em>Vertex Form</em> by completing the square, using this formula to get part of your new C-term:
When done, you get this:
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:
From here, we can see that our vertex is [-2, -9].
a) When the binomial is set to equal to zero, you get this:
e) <em>See above photograph</em>
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