Answer:
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Step-by-step explanation:
the picture
The vertex is (-1,1)
Explanation
The vertex formula to find the x coordinate of the formula is -b/2a
So we plug in the values into the formula which is
-4/2(2)
Simplify it
-4/4
=-1
-1 is now the x cord of the vertex.
So now we will plug in the x into the quadratic equation which is 2x^2+4x+3
2(-1)^2 + 4(-1) + 3 = 2 -4 +3
Simplify it
5 - 4= 1
Y=1
So the Coordinates of the vertex is (-1,1)
Discriminant, D = b² - 4ac
x² - 4x + 5 = 0 comparing to ax² + bx + c = 0
a = 1, b = -4, c = 5
D = b² - 4ac = (-4)² - 4*1*5 = 16 - 20 = -4
In taking the square root of the discriminant of -4, √-4 = 2i = Not Real. So:
Discriminant is -4, so the equation has no real roots.
The second option is correct.
