Given the x-intercepts, (-6, 0) and (-1, 0):
Use the quadratic equation in intercept form:
y = a(x - p)(x - q)
where a is the same value as in standard form, p and q are the x-intercepts, or where the graph passes through the x-axis.
Substitute the values into the equation:
y = a(x - p)(x - q)
y = a(x + 6) (x + 1)
To find the value of a, use the coordinates of the y-intercept, (0, 6) and substitute in the equation:
y = a(x + 6) (x + 1)
6 = a(0 + 6) (0 + 1)
6 = a(6)(1)
6 = 6a
Divide both sides by 6 to solve for a:
6/6 = 6a/6
1 = a
Therefore the quadratic equation in factored form is:
y = (x + 6) (x + 1)
Attached is a screenshot of the graphed parabola using the equation, y = (x + 6) (x + 1), where it shows the given points (intercepts).
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