Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.

Question

yequalsnegative 2 x squared plus 7 x minus 3
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Part 1
The axis of symmetry is xequals
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

x = -b/(2a)
x = -7/(2*(-2))
x = -7/-4
x = 7/4

Therefore, the axis of symmetry is x = 7/4.

Answer 2

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
yequalsnegative 2 x squared plus 7 x minus 3
Question content area bottom
Part 1
The axis of symmetry is xequals
  
seven fourths
. ​(Simplify your​ answer.)
Part 2
The vertex is
  
enter your response here.
​(Type an ordered pair. Simplify your​ answer.)

Answer 3

Part 2:
To find the y-coordinate of the vertex, substitute the x-coordinate of the axis of symmetry into the equation:

y = -2(7/4)^2 + 7 * (7/4) - 3
y = -2(49/16) + 49/4 - 3
y = -98/16 + 49/4 - 3
y = -98/16 + 196/16 - 48/16
y = 50/16
y = 25/8

Therefore, the vertex is (7/4, 25/8)