y = ax^2 + bx + 5; (-1,4), Finding a and b?

y(-1) = a - b + 5 = 4

a - b = -1 => a = b - 1

-b/a = -b/(b - 1)

c/a = 5

a = 1

b = 2

y = x^2 + 2x + 5

If (-1,4) is the vertex then the function can be written as y = (x + p)^2 + q

The x co-ordinate makes the bracket zero and q is the y co-ordinate of the vertex.

So, y = (x +1)^2 + 4

Expanding and simplifying gives:

y = x^2 + 2x + 5, so a = 1 and b = 2 ....resulting in a parabola with minimum point at (-1,4)

If (-1,4) is onto your parabola then

4 = a*(-1)^2 - b*(-1) + 5

a-b = -1

b = a+1

Then

y = ax^2 +(a+1)x+5

This is a parabolas family and passes to (-1,4)

You must have 2 points to find a and b for parabola y = ax^2 + bx + 5

y = ax^2 + bx + 5; (-1,4)

Find a and b

4 = a - b + 5

a -b = 4 -5 .................... [1]

Analysing [1], we get,

a = 4, and b = -5 >=================< ANSWER

y = ax^2 + bx + 5; (-1,4)

y = (x + 1)(x - 4)

y = x^2 - 3x - 4

Find a and b

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Q2. The quadratic formula states 2 recommendations: they are (-b+ sqrt(b^2-4ac))/2a and (-b- sqrt(b^2-4ac))/2a. a stands for the coefficient of the squared term, b stands for the coefficinet of the 1st degree term, and c stands for the consistent term. subsequently as a effect a=2. b=a million, and c=-6 subsequently the recommendations are ( -a million+sqrt(a million+24))/4 = ( -a million +5)/4 = a million and (-a million -sqrt(a million+24))/4 = ( -a million -5)/4 = -3/2 Q1. here use the comparable formula (when you write the equation in the excellent suited sort, that's y^2+5y-14=0).

replace the coords in the eqns:

4= a(-1)^2+b(-1) +5

4=a^2-b+5

a^2-b= -1

a^2 = b-1

a= ±√ (b-1)

b=a^2+1