The y-component of the vertex is -10
The x-component of the vertex is -1 and 5
The discriminant of the quadratic function is -16
Given the quadratic function f(x) = 2x² – 8x – 10.
The x-component of the vertex is the point where f(x) = 0
f(x) = 2x² – 8x – 10
2x² – 8x – 10 = 0
Factorize;
2x² – 10x +2x – 10 = 0
2x(x - 5) + 2(x-5) =0
(2x+2) (x-5) =0
2x = -2 and x = 5
x = -1 and 5
The x-component of the vertex is -1 and 5
The y-component of the vertex is the point where x = 0
f(x) = 2x² – 8x – 10
f(0) = 2(0)² – 8(0) – 10
f(0) = -10
Hence the y-component of the vertex is -10
From the quadratic expression, a = 2, b = -8 and c = 10
Discriminant = b^2 - 4ac
Discriminant = (-8)^2 - 4(2)(10)
Discriminant = 64 - 80
Discriminant = - 16
Hence the discriminant of the quadratic function is -16
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