Question

Match the given quadratic function y=ax²+bx+c to its equivalent standard form y=a(x-h)²+k.

y=x²-x+13/4
y=½x²-3x+3
y=-2x²+12x-17
y=x²-4x+1
y=2x²-4x+4
y=(x-2)²-3
y=2(x-1)²+2
y=-2(x-3)²+1
y=(x-½)²+3
y=½(x-3)²-3/2​

Answer 1

Answer:

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Answer 2

The standard form of any quadratic equation can be represented in the form;

y=a(x-h)²+k

in which (h, k) are the vertices. and since a vertex appears in the standard form of the equation therefore it is also called vertex form of quadratic equation.

If a in the given equation is positive that is a>0 then the parabola opens upwards.

whereas if a<0 then parabola opens downward.

Usually we get the quadratic equation like:

f(x) = ax^2+bx+ c, where, a, b, c are real number and a is not equal to 0 .

to convert it in standard form we can use the following way to find h and k

h= -b/2a and k= f(-b/2a)

Now the standard form of the given quadratic equation will be :

1.) y=x²-x+13/4

Ans. y=(x-½)²+3

2.) y=½x²-3x+3

Ans. y=½(x-3)²-3/2

3.) y= -2x²+12x-17

Ans. y= -2(x-3)²+1

4.) y=x²-4x+1

Ans. y=(x-2)²-3

5.) y=2x²-4x+4

Ans. y=2(x-1)²+2