James is supposed to feel his dog 1 1/3 cups of dog food every day. James doesn’t want his dog to eat all of the food at once, s
1 answer:
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Answer:
y = x^2 +6x +8
Step-by-step explanation:
The vertex is (-3, -1), and the vertical scale factor is 1. (You can tell this because the graph goes up 1 unit for 1 unit either side of the vertex.) So, the vertex form of the equation is ...
y = (x +3)^2 -1 . . . . . . . . . vertex form; sometimes called standard form
Expanding this, we get ...
y = x^2 +6x +8 . . . . . . . . also called the standard form equation
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<em>Comment on standard form</em>
There are different versions of "standard form" depending on what you're concerned with and where you are. Please consult your text or other reference material for the version of standard form you need. (The attachments show the conflict with respect to quadratic equations.)
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<em>Comment on the graph</em>
The purpose of the graph attached is to show that the equation we propose produces the same curve as the one given.
Answer:
Step-by-step explanation:
Since AC || DE, and ABC forms a triangle, we can deduce that ABC is a smaller triangle inside triangle DBE.
In the second step, we see that ∠CAB in the smaller triangle is congruent to ∠EDB in the larger one, due to the corresponding angles theorem. We also see that ∠ACB in the smaller triangle is congruent to ∠DEB in the larger one, again by the corresponding angles theorem.
This leads to the third step; since we have two of the angles in one triangle congruent to the corresponding angles in the other triangle, this means the third angle will be congruent (since all triangles equal 180°, and the first two angles are equal, the third must be equal as well). Two triangles in which all three angles of one triangle are congruent to the three angles of the other are similar triangles.
Since the triangles are similar, corresponding sides have the same ratio. This means that the ratio of AB to the larger side DB is the same as the ratio of CB to the larger side EB; this gives us
AB/DB = CB/EB.