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How many times will the graph of y equals x2 plus 6x plus 9 cross the x axis?
Wiki User
∙ 11y ago
None, it touches it at x = -3.
For a quadratic y = ax2 + bx + c, it will meet the x-axis (y = 0) either 0, 1 or 2 times dependent on: b2 - 4ac. If b2 - 4ac is:
- > 0 the line meets the x-axis twice, so crosses it twice
- = 0 the line meets the x-axis once, so it does not cross it but only meets it.
- < 0 the line does not meet the x-axis at all, so cannot cross it.
for y = x2 + 6x + 9:
b2 - 4ac = 62 - 4 x 1 x 9
= 36 - 36
= 0
so the line meets the x-axis once, but does not cross it - all the values of y are greater than, or equal to zero, but never negative.
Wiki User
∙ 11y ago
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