SOLUTION: Given the quadratic function y = x 2 - 4 x + 3 , respond to the following: a) Does the graph open up or down? b) What is the equation of the axis of symmetry? c

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Given the quadratic function y = x 2 - 4 x + 3 , respond to the following: a) Does the graph open up or down? b) What is the equation of the axis of symmetry? c      Log On


   

Question 35924: Given the quadratic function y = x 2 - 4 x + 3 , respond to the following:
a) Does the graph open up or down?
b) What is the equation of the axis of symmetry?

c) What are the coordinates of the vertex?
d) Give the y intercept.
e) Give the x intercept(s).
f) Sketch the graph
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
y++=++x%5E+2++-+4+x++%2B++3

This is a parabola that opens up, since the coefficient of x%5E2 is positive.

You can complete the square or use a formula x+=+-b%2F%282a%29+ to find the vertex and the line of symmetry.

Completing the square looks like this:
y++=++x%5E+2++-+4+x++%2B++3

Take half of the x coefficient (which is -2) and square it (which is 4), and add and subtract 4 from the right side of the equation.

y++=++x%5E+2++-+4+x++%2B+_____%2B++3+-+_____
y++=++x%5E+2++-+4+x++%2B+4%2B++3+-+4
y+=+%28x-2%29%5E2+-1

The line of symmetry will be the value of x that "zeros out the %28x-2%29%5E2%29+, which will be x=2. This will also be the x coordinate of the vertex. To find the y coordinate of the vertex, let x= 2, and you have y = -1.

Vertex = (2,-1)

The y intercept is where x = 0. If x = 0, then y =3.

The x intercept is where y = 0. If y = 0, then
0=+x%5E2+-+4x%2B3
0+=+%28x-3%29%28x-1%29
So, the x intercepts will be at x =3 and x= 1.

Graph graph%28300%2C300%2C+-4%2C+8%2C+-4%2C10%2C+x%5E2+-4x%2B3%29+

R^2 at SCC