There is going to be a question like this on a test this week and if someone can show me how to do this one, hopefully I'll understand...For the graph of function, find an equation of the line of...

There is going to be a question like this on a test this week and if someone can show me how to do this one, hopefully I'll understand...
For the graph of function, find an equation of the line of symmetry and the coordinates of the vertex. Tell whether the value of the function at the vertex if a maximum or a minimum:
a. y=-x^2+4x-7;
b. y=2x^2+4x;
c. y=-3x^2-18x+5

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violy | High School Teacher | (Level 1) Associate Educator

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For the vertex (h, k) we will use the formula:  h = -b/(2a) and k = f(h). For the axis of symmetry it will be x = h. 

For letter a:

Identify a, b and c. The given equation is in the form y = ax^2 + bx + c. 

So, a = -1, b = 4 and c = -7. 

We will have: h = -(4)/(2(-1)) = -4/-2 = 2. 

For the value of k, we plug-in 2 in replace of x's in the original equation. k = -(2)^2 + 4(2) - 7 = -4 + 8 - 7 = -3

Therefore, vertext is (2, -3), and line of symmetry is at x = 2. We will have a maximum at the vertex since the sign of our a is negative. It means that the parabola opens downward. 

For the second equation. 

a = 2, b = 4 and c = 0.

So, h = -(4)/2(2) = -4/4 = -1.

For the k = 2(-1)^2 + 4(-1) = 2 - 4 = -2. 

Therefore, vertext is (-1, -2), and line of symmetry is at x = -1. We will have a minimum at the vertex since the sign of our a is positive. It means that the parabola opens upward. 

For the third equation. 

a = -3, b = -18 and c = 5.

So, h = -(-18)/2(-3) = 18/-6 = -3.

For the k = -3(-3)^2-18(-3)+5 = -27 + 54 + 5 = 32. 

Therefore, vertext is (-3, 32), and line of symmetry is at x = -3. We will have a maximum at the vertex since the sign of our a is negative. It means that the parabola opens downward. 


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