Which of the following points represents the x-intercepts of the quadratic equation y = x2 + 5x + 6?
Question
Which of the following points represents the x-intercepts of the quadratic equation
?
Solution
The x-intercepts of a quadratic equation are the values of x for which y = 0.
So, to find the x-intercepts of the equation y = x^2 + 5x + 6, we set y = 0 and solve for x:
0 = x^2 + 5x + 6
This is a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = 5, and c = 6.
We can solve this equation by factoring:
0 = (x + 2)(x + 3)
Setting each factor equal to zero gives the solutions x = -2 and x = -3.
So, the x-intercepts of the equation y = x^2 + 5x + 6 are the points (-2, 0) and (-3, 0).
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