# Give the quadratic functions y=x2 - 2x - 3 and y = -x2 + 4x - 1, transform them into the form y=a(x-h)2+k.

1
by aisahmangata

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2015-09-27T12:48:48+08:00

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Vertex of parabola/graph of quadratic equation = (h,k)

h = -b/2a
k = 4ac - b²
4a

1) y = x² - 2x - 3
a = 1;   b = -2;   c= -3

h = -(-2)/ 2(1)
h = 2/2
h = 1

k = 4ac - b²
4a
k = 4(1)(-3) - (-2)²
4(1)
k = - 12 - 4
4
k = -16/4
k = - 4

Vertex form : a (x-h)² + k,  substitute the values for h and k:

Vertex form: a(x-1)² - 4

2) -x² + 4x-1
a = -1;   b = 4;    c= -1

h = -(4)/2(-1)
h = -4/-2
h = 2

k = 4(-1)(-1) - (4)²
4(-1)
k = 4 - 16
-4
k = -12/-4
k = 3

Vertex form:  Substitute the values for h and k:

Vertex form:  - (x-2)² + 3