![]() The number in front of the \(x\) is the gradient of the graph.Īs you move along a line from left to right, you might go up, you might go down or you might not change at all. The graphs \(y = 2x\) and \(y = 4x\) are shown below: This is known as the \(y\) -intercept and is represented by the letter \(c\) in \(y = mx c\). The constant term in the equation (the 1 or ‒ 2) shows the point where the graph crosses the \(y\) -axis. The graph of \(y = 2x 1\) crosses the \(y\) -axis at (0, 1). ![]() The graphs of \(y = 2x 1\) and \(y = 2x - 2\) are shown below. \(m\) is the gradient, or steepness of the graph, and \(c\) is the \(y\) - intercept, or where the line crosses the \(y\) -axis. The y intercepts of a curve are the points at which the curve intersects the y -axis (i.e. The graph of this function is a line with slope and y -intercept The functions whose graph is a line are generally called linear functions in the context of calculus. It has therefore a unique solution for y, which is given by This defines a function. Put a =2, b = -1, c = 3 in the standard form of parabola equationįind a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.Any equation that can be rearranged into the form \(y = mx c\), will have a straight line graph. is a linear equation in the single variable y for every value of x. Substitute b = -1 c = 3 in the third equation ![]() When the parabola passes through the point (-1,6), then 6 = a – b c Just like the y-intercept, the x-intercepts are basically the points where the graph of a function or an equation touches or passes through the x-axis of the Cartesian Plane. In a point notation, it is expressed as (0,y) How to Find the X-Intercepts. When the parabola passes through the point (2,9), then 9 = a(2) 2 b(2) c = 4a 2b c In order to determine the y-intercepts of an equation, let x 0, then solve for y. When the parabola passes through the point (1,4) then, 4 = a b c The standard form of the equation of the parabola is y = ax 2 bx c Question 2: Find the equation, focus, axis of symmetry, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the parabola that passes through the points (1,4), (2,9), (−1,6)? To get x-intercept put y = 0 in the equation To get y-intercept put x = 0 in the equation The focus of x coordinate = -b/ 2a = -2/5įocus of y coordinate is = c – (b 2 – 1)/ (4a)ĭirectrix equation y = c – (b 2 1) / (4a) The parabola equation in vertex form is y = a(x-h) 2 k The standard form of the equation is y = ax 2 bx c Given Parabola equation is y = 5x 2 4x 10 Question 1: Find vertex, focus, y-intercept, x-intercept, directrix, and axis of symmetry for the parabola equation y = 5x 2 4x 10? ![]()
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