Question

I just need my work checked and a couple questions answered please.(The Question was find the vertex Form of the equation.)Y=-x^2 + 12x-4Use the form ax^2+bx + ca=1, b=12, c =-4a(x+d)^2+e ( is it wrong to use this in this problem to answer the question ?) d=b/2ad= 12/2 x -1Then I cancel the common factor of 12 and 2d= 2 x 6/2 x -1Then move the negative one from the denominator of 6/-1d=-1 x 6, then I multiply d=-6Then I Find the value of e using the formula e= c- b^2/4ae=-4 - 12^2/4 X-1e=-4 - 144/4 x-1e=-4 - 144/-4Divide 144 by -4e=-4 - -36Multiply -1 by -36e= -4+36, Than adde= 32Then substitute the values of a, d, e into the vertex formAnswer isY=-(x-6)^2+ 32*********1. Is this the correct way of doing this problem? this is what my tutor taught me?2. Should I have not useda(x+d)^2+ e. In this problem ?3.What is a (x+d)^2+ e called? And when should you use it?4. Is there an easier way?

Answer 1

The vertex form of a quadratic equation is expressed as

y = a(x - h)^2 + k

where

h and k are the x and y coordinates of the vertex of the curve formed.

a is the leading coefficient

The standard form of a quadratic equation is written as

y = ax^2 + bx + c

The given equation is

y = - x^2 + 12x - 4

By comparing the given equation with the standard form equation, we have

a = - 1

b = 12

c = - 4

We would find the x coordinate of the vertex by applying the formula,

x = - b/2a

By substituting the given values into this formula, we have

x = - 12/2 * - 1 = - 12/- 2 = 6

We would find the y coordinate of the vertex by substituting x = 6 into the given equation. We have

y = -(6)^2 + 12(6) - 4

y = - 36 + 72 - 4

y = 32

Thus,

x = h = 6

y = k = 32

a = - 1

By substituting these values into the vertex form equation, the equation in vertex form is

y = - (x - 6)^2 + 32

1) The method used was quite different. It is correct although there were some mistakes in the work.

2) Using a(x + d)^2 + e is like using a(x - h)^2 + k but the terms inside the parentheses should have been x - d

3) a (x+d)^2+ e cannot be called the 'vertex form' of a quadratic equation because the parenthses has x + d instead of x - d

4) The shorter way is the method that i used