Solve by graphing x^2-6x+5=0
2 answers:
Answer:
x = 1 and x = 5
Step-by-step explanation:
First we find the axis of symmetry. This will be a dotted line marking where the graph will "fold" in half. To find this we use the formula x = -b/2a:
x = -(-6)/2(1) = 6/2 = 3
We draw a dotted line at x=3, as seen in the first screenshot.
Next we find the vertex. Substitute the value of x into the related equation,
y = x²-6x+5
y = 3²-6(3)+5 = 9-18+5 = -9+5 = -4
The y-coordinate of the vertex is at -4, making the vertex (3, -4); this is seen in the second screenshot.
Next we graph the y-intercept; this is c in the equation, which in this equation is 5. This is seen in the third screenshot.
Next we reflect the y-intercept through the axis of symmetry; this is seen in the fourth screenshot.
Lastly we connect these three points with the parabola, or u-shaped graph. This is seen in the fifth screenshot.
To find the solutions, we find the x-intercepts. We can see from the fifth screenshot that these are at x=1 and x=5; these are the solutions.
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