Consider the quadratic equation: y = 4x^2 - 4x - 5?
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The equation of the axis of symmetry of y=2x^2-7x+5 is?
The vertex of this parabola is = -b/2a where, b = -7 and a = 2 vertex at x = -(-7) / 2*2 = 7/4 at x = 7/4 => y = 2(4)^2 - 7(4) + 5 = 9 vertex is (7/4 , 9) the symmetry line is the line parallel to y axis. therefore , x = 7/4
How do I find a quadratic equation given 2 points and no vertex?
While it is true that three equations are needed to find the three coefficients, some conditions might help develop a specific equation. However, you are asking “a” quadratic equation.Assuming a vertical axis of symmetry, the equation would be of the form y = ax^2 + bx + c which can also be written as y = a(x - h)^2 + k.Case 1: If the two points have the same y value,then the axis of symmetry will pass through the midpoint of the segment between them. For example, if the given points are (1, 7) and (5, 7), then the midpoint is found by averaging the x coordinates. (1 + 5)/2 = 3. The axis of symmetry is x = 3.Two equations can then be written from the given points(1, 7) 7 = a(1 - 3)^2 + k or 7 = 4a + k(5, 7) 7 = a(5 - 3)^2 + k or 7 = 4a + kAs expected, we have only one equation with two unknowns, resulting in no particular solution. However, once again, looking for a solution, choose a value for k, say -5, the equation becomes 7 = 4a - 512 = 4aa = 3The equation becomes y = 3(x - 3)^2 -5which becomes y = 9(x^2 -6x +9) -5and then y = 9x^2 -54x + 76.Case 2: If the two points have the same y value,Example (1, 7) and (3, 31)7 = a(1)^2 + b(1) + c and 31 = a(3)^2 + b(3) +c(1) 7 = a + b + c and (2) 31 = 9a + 3b + cSubtracting equation 1 from equation 224 = 8a + 2bdividing by 212 = 4a + bb = 12 - 4aLet a = 2 or any other chosen valueb = 12 - 4(2)b = 4Substituting into equation 17 = (2) + (4) + cc = -1Answer: An equation going through the two points is y = 2x^2 + 4x - 1
Convert this math equation to vertex form and then find the axis of symmetry and vertex: y= 2x^2+8x-4?
y=2x^2+8x-4; Y = 2*X^2+8*X-4 Standard form: a(X-h)²+k = (2X² +8X +8) -8 -4 = 2(X +2)² -12 X = -2 ±√(6) = -4.449489742783178, or 0.4494897427831779 Axis of symmetry: X= -2; Vertex (minimum): ( -2, -12); y-intercept is (0,-4) Quadratic formula: X = (-b ±√(b²-4ac))/(2a) = ( -8±√(64 +32))/(4) positive discriminant = 96; two real roots: X=-4.449489742783178 and 0.4494897427831779 factors: (2X -0.898979486)(X +4.449489743) = 2 (X -0.449489743)(X +4.449489743)
Rewrite the equation y=4x^2-4x-5 in vertex form. Name the vertex and the axis of symmetry.?
y = 4x^2 - 4x - 5 y = 4(x^2 - x) - 5 y = 4(x^2 - x + 1/4) - 5 + 1 y = 4(x - 1/2)^2 - 4 The vertex is (1/2, -4) and the axis of symmetry is x = 1/2.