Answer:
a = 3/4
Step-by-step explanation:
Given the vertex, (3, -1) and the other point, (5, 2):
We could substitute these values into the vertex form of the quadratic equation:
y = a(x - h)² + k
Where:
(<em>h</em>, <em>k </em>) = vertex
<em>a </em>= determines whether the graph opens up or down, and makes the graph wider or narrower.
- If a is <u>positive</u>, the graph opens up; if a is <u>negative</u>, the graph opens down.
- If a is between 0 and 1, the graph is <u>wider</u> than the parent function.
- If a > 1, the graph is <u>narrower</u> than the parent function.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em><em> = </em>determines how far up or down the parent function is translated.
Substitute the vertex, (3, -1) and point (5, 2) into the vertex form to solve for "a":
y = a(x - h)² + k
2 = a(5 - 3)² - 1
2 = a(2)² - 1
2 = a(4) - 1
Add 1 to both sides:
2 + 1 = a(4) - 1 + 1
3 = 4a
Divide both sides by 4 to solve for a:
3/4 = 4a/4
3/4 = a
Therefore, the value of a = 3/4. Since the value of a is positive, and that it is between 0 and 1, then it means that the graph opens upward and is wider than the parent function.
The quadratic equation in vertex form is: y = 3/4(x - 3)² - 1, where a = 3/4.
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