SOLUTION: What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$?
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
Your answer shoul
Question 1209639: What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$?
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
Your answer should be a list of numbers and should not include variable names, nor should it include $y$-coordinates. Answer by ikleyn(52780) (Show Source):
You can put this solution on YOUR website! .
What are the x-coordinate(s) of all point(s) where the parabola y = f(x) intersects the line y = 0?
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
Your answer should be a list of numbers and should not include variable names, nor should it include $y$-coordinates.
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(1) Simplify f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7 = -3x^2 + 6x + 27.
(2) The intersection points of the parabola with the line y = 0
are the points on x-axis where -3x^2 + 6x + 27 = 0.
In Algebra language, these points are called the roots of the equation
-3x^2 + 6x + 27 = 0.
In other terminology, these points are called x-interception points.
(3) So, your task is to solve this equation
-3x^2 + 6x + 27 = 0.
To simplify, divide both side by the common factor -3. You will get an EQUIVALENT equation
x^2 - 2x - 9 = 0.
Apply the quadratic formula
= = = .
(4) So, the roots of the given equation are
= = -2.162 (rounded) and = = 4.162 (rounded).
They are x-coordinates of the intersection points.
