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The graph of the quadratic y = ax^2 + bx + c has the following properties: (1) The maximum value of y = ax^2 + bx + c is 5, which occurs at x = 3. (2) The graph passes through the point (0,8). If the graph passes through the point (4,m), then what is the value of m?

 Jun 23, 2021
 #1
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Let's put ax^2 + bx + c into the form a(x-h)^2 + k because I think it's easier to work with. 

 

 

(1) The maximum value of y = ax^2 + bx + c is 5, which occurs at x = 3.

That means that a is a negative value, that h = 3, and that k = 5. 

a(x-3)^2 + 5

 

(2) The graph passes through the point (0,8).

8 = a(0-3)^2 + 5

 

Next, you want to solve for a, and then find m by plugging in x = 4. 

 

=^._.^=

 Jun 23, 2021

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