Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
yequals2 x squared minus 5 x plus 4
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Part 1
The axis of symmetry is xequals
five fourths
. (Simplify your answer.)
Part 2
The vertex is
enter your response here.
(Type an ordered pair. Simplify your answer.)
Part 1:
The axis of symmetry is x = 5/4
Part 2:
To find the vertex, we first need to find the x-coordinate using the formula x = -b/2a, where a = 2 and b = -5 from the given function y = 2x^2 - 5x + 4.
x = -(-5)/(2*2) = 5/4
Now, substitute x = 5/4 back into the original function to find the y-coordinate:
y = 2(5/4)^2 - 5(5/4) + 4
y = 2(25/16) - 25/4 + 4
y = 50/16 - 100/16 + 64/16
y = 14/16
Therefore, the vertex is (5/4, 14/16) or (5/4, 7/8).