Antonia wants to buy a television that costs $600, including taxes. To pay for the television, she will use a payment plan that
1 answer:
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9514 1404 393
Answer:
y = 1/2x^2 +x -15/2
Step-by-step explanation:
The vertex is the point where the graph reaches is extreme: (-1, -8). The y-intercept is (0, -7.5). The x-intercepts are (-5, 0) and (3, 0).
When the quadratic is written in the form ...
y = x^2 +bx +c
the value of b is the opposite of the sum of the x-intercepts. The value of c is their product. These facts would give ...
y = x^2 -(-5 +3)x +(-5)(3) = x^2 +2x -15
The constant in this equation is -15, which is the value y has when x=0. Our actual y-intercept is half that, so the graph we see is this equation scaled by a factor of 1/2:
y = 1/2x^2 +x -15/2
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<em>Alternate solution</em>
You can start with the vertex form.
y = a(x -h)^2 +k . . . . . . . vertical scale factor 'a' and vertex (h, k)
On the graph, the vertical scale factor is the vertical difference between the low point (vertex) and the point that is 1 unit right or left. Here, that is ...
-7.5 - (-8) = 0.5 = a
We've already said the vertex is (h, k) = (-1, -8), so the vertex form equation is ...
y = 0.5(x +1)^2 -8
We know the square of a binomial is (a+b)^2 = a^2 +2ab +b^2, so we have ...
y = 0.5(x^2 +2x +1) -8
y = 0.5x^2 +x +0.5 -8 . . . . . eliminate parentheses
y = 0.5x^2 +x -7.5
Option C: (x+4) and (x-1) are the factors of the equation
Explanation:
Given that the equation is
We need to determine the factors of the equation.
Splitting the middle term, we get,
Grouping the terms, we have,
Let us factor out the term (x+4), we have,
Thus, the factors of the equation are (x+4) and (x-1)
Hence, Option C is the correct answer.