-x^(2)-12=-87 Please explain your answer, and how I make the x positive
1 answer:
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Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
is provided, so statement 1 pairs with the reason "Given".
Since perpendicular lines, by definition, form right angles where they meet, and ∠T is one of those meeting angles, we can match statement 2 with the 4th reason on the list, "Perpendicular lines form right angles"
In any right triangle, the two angles apart from the right angle must add to 90° which, except in the case where one of those angles is 0°, means that both must measure less than 90°. Since ∠R is one of those acute angles, we can say that m∠T > m∠R, so we can match statement 3 with reason 2, "The measure of a right angle is greater than the measure of an acute angle."
All triangles have the property that, given two interior angles, one bigger than the other, <em>the side opposite the bigger angle will be bigger than the side opposite the smaller one</em>. With this knowledge, we notice that since m∠T > m∠R, the side across from ∠T, , must be bigger than the side across from ∠R,
. We can then match statement 4 with reason 1, which says the same thing.