Use the graph of y = x2 + 4x - 5 to answer the following:?

Question

a) What is the solution to x2 + 4x -5 =0 ?

b) Does this function have a maximum or a minimum ?

c) What are the coordinates of the vertex in (x,y) form ?

d) What is the equation of the line of symmetry for this graph ?

Answer 1

I suggest you to rewrite the function into this form:

pow(x#2)+4*x-5

and then enter it to

http://rechneronline.de/function-graphs/

I recommend to adjust the ranges of x- and y-axes from -10 to 10.

You may also play with it, change the parameters of the function and observe how it change the shape of the curve. Three curves of different color may be seen simultaneously.
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Answer 2

a) What is the solution to x^2 + 4x -5 =0 ?

Factor- = (x-1)(x+5) therefore x = (1,-5) are where the graph crosses the x-axis.


b) Does this function have a maximum or a minimum ?

Yes. It is an upward-opening parabola with a minimum midway between the x-axis crossings, which is at

x = (1 - 5)/2 = -4/2 = -2


c) What are the coordinates of the vertex in (x,y) form ?

Substituting in x = -2, the y-coordinate of the vertex will be

(-2)^2 + 4(-2) -5 =

4 - 8 - 5 = -9, so vertex is at (-2, -9)


d) What is the equation of the line of symmetry for this graph ?

x = -2

Answer 3

(a) Its a parabola that crosses the x axis twice, so it has two solutions. It crosses the x axis at x=1 and at x = -5. So the two solutions are x=1 and x = -5. There are other ways of finding this, but in your instructions it says "use the graph".

(b) Minimum value, no maximums

(c) (-2, -9)

(d) The line of symmetry is a vertical line stemming from the vertex of the parabola. So x = -2 is our line.

Answer 4

a) factor the expression
= (x+5)(x-1)
then this ==0 at x=-5 and at x=1

b) has a minimum because it is a positive quadratic. There are no maxima.

c)The vertex, here, is the midpoint between the roots.
x(vertex) = -3
y(vertex) = (-3)^2 +4(-3) - 5
y = 9-12-5
y = -8
(x,y) = (-3,-8) vertex coords

d)
x = -3

Answer 5

a.) x^2+4x-5=0
x^2+4x+4=9
(x+2)^2=9
x+2=+-3
x=-5, 1
b.)it has a minimum because the parabola opens upwards.
c.)y=x^2+4x-5
=(x^2+4x+4)-9
=(x+2)^2-9
vertex:(-2,-9)
d.) x = -2