SOLUTION: identify the vertex,axis of symmetry and intercepts (if they exist) of the function: x^2-4x+2

Question 519298: identify the vertex,axis of symmetry and intercepts (if they exist) of the function: x^2-4x+2
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
y = x^2 -4x + 2
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A graph will help visualize the problem and the solution.
.

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Note that y = x^2 -4x +2 is n the form: y = ax^2 + bx +c
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Axis of symmetry is the value of x, where
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x = -b/2a is the known formula
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substitute b= -4 and a=1
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x = -(-4)/(2*1) = 4/2 = 2
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Vertex is the (x,y) coordinate, where the value of x from above is substituted
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y = x^2 -4x +2
y = (2)^2 -4(2) + 2
y = 4 -8 +2
y = -2
so the vertex is
(2,-2)
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The y-intercept occurs when x=0
y = 2, which is the point (0,2)
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To find the x-intercepts you have to solve:
0 = x^2 -4x +2
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This equation does not factor, so to find the intercepts use the quadratic equation
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=8 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.41421356237309, 0.585786437626905. Here's your graph:

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