Question

2. Find the value of "a" given the vertex and a second point when the vertex is (3,-1) and the graph passes through (5, 2)

Answer 1

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:

(h, k ) = vertex

a = determines whether the graph opens up or down, and makes the graph wider or narrower.  

• If a is positive, the graph opens up; if a is negative, the graph opens down.

• If a is between 0 and 1, the graph is wider than the parent function.
• If a > 1, the graph is narrower than the parent function.

h = determines how far left or right the parent function is translated.

k =  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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