Is It Safer To Drive Or Get On A Plane?
2 answers:
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Given:
The x- intercepts of a parabola are (0,-6) and (0,4).
The parabola crosses the y- axis at -120.
Lucas said that an equation for the parabola is and that the coordinates of the vertex are (-1, -125).
To find:
Whether Lucas is correct or not.
Solution:
The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.
...(i)
The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).
Divide both sides by -24.
Substituting in (i), we get
So, the equation of the parabola is .
The vertex of a parabola is:
In the equation of the parabola, .
Putting in the equation of the parabola, we get
So, the vertex of the parabola is at point (-1,-125).
Therefore, Lucas is correct.
The complete question: <span>Megan bikes 6 miles west to get from her apartment to school. After school, she bikes 8 miles north to her friend's house. How far is Megan's apartment from her friend's house, measured in a straight line?
So,Megan's apartment, the school, and Megan's friend's house form a right triangle with legs 6 miles and 8 miles as you can see in the attached picture; the hypotenuse of the right triangle is the straight distance is from Megan's apartment to her friend's house. To find that distance we are going to use the Pythagorean theorem:
</span>
<span>
We can conclude that distance between Megan's apartment and her friend's house is 10 miles.</span>
So,Megan's apartment, the school, and Megan's friend's house form a right triangle with legs 6 miles and 8 miles as you can see in the attached picture; the hypotenuse of the right triangle is the straight distance is from Megan's apartment to her friend's house. To find that distance we are going to use the Pythagorean theorem:
</span>
<span>
We can conclude that distance between Megan's apartment and her friend's house is 10 miles.</span>