The equation must have roots of x = -1 and x = 5
So: x + 1 = 0 and x - 5 = 0
Therefore: (x + 1)(x - 5) = 0
Expanding the brackets gives the equation:
x2 - 4x - 5 = 0
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It is: (2x-5)(2x-5) = 2.5 square cm when solved as a quadratic equation
Equation: 10x^2 -29x +10 = 0 When factored: (2x-5)(5x-2) = 0 Its solutions: x = 5/2 or x = 2/5
Known equation: 3x+5y = 6 or y = -3/5x +6/5 Slope of equation: -3/5 Slope of parallel equation: -3/5 Parallel equation: y-1 = -3/5(x-3) => 5y = -3x+14 Parallel equation in its general form: 3x+5y-14 = 0
Since we know the slope, m = 5/3, and the y-intercept 1/2, we arw able to write the equation of the line in the slope-intercept form, y = mx + b, so we have y = (5/3)x + 1/2.The standard form of the equation of the line is Ax + By = C.y = (5/3)x + 1/2y - y - 1/2 = (5/3)x - y + 1/2 - 1/2-1/2 = (5/3)x - y or(5/3)x - y = -1/2Thus, the standard form, Ax + By = C, of the equation of the line is (5/3)x - y = -1/2.
A quadratic equation is an equation with the form: y=Ax2+Bx+C The most important point when graphing a parabola (the shape formed by a quadratic) is the vertex. The vertex is the maximum or minimum of the parabola. The x value of the vertex is equal to -B/(2A). Once you have the x value, just plug it back into the original equation to get the corresponding y value. The resulting ordered pair is the location of the vertex. A parabola will be concave up (pointed downward) if A is +. It will be concave down (pointed upward) if A is -. It is often helpful to find the zeroes of a function when graphing. This can be done by factoring or using the quadratic formula. For every n units away from the vertex on the x-axis, the corresponding y value goes up (or down) by n2*A. Parabolas are symetrical along the vertex, which means that if one point is n units from the vertex, the point -n units from the vertex has the same y value. As an example take the following quadratic: 2x2-8x+3 A=2, B=-8, and C=3 The x value of the vertex is -B/2A=-(-8)/(2*2)=2 By plugging 2 into the original equation we get that the vertex is at (2,-5) 3 units to the right (x=5) has a y value of -5+32*2=13. This means that 3 units to the left (x=-1) has the same y value (-1,13). If you need a clearer explanation, ask a math teacher.