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Parabola,maths jee , class
What is the equation of the axis of symmetry of the parabola given by the equation y = 6(x + 1)(x - 5)? a. y = 2 b. x = - 2 c. y = - 2 d. x = 2 Explanation The axis of symmetry lies directly between the two roots. You can find it on a graph by working your way to the middle or algebraically by calculating the average between the two points: x = (p + q)/2. For y = 6(x + 1)(x - 5) To find p and q, remember to change the sign of each number. (Think of it as (x + 1 = 0). Therefore x = - 1 and (x - 5 = 0) (Thus, x = 5) p = - 1 q = 5 x = (-1 + 5)/ x = 2
x = 2 Given the following equation, y = 3(x + 5)(x + 9), x = 5 & x = 9 are _____. a. not the x-intercepts b. the y-intercepts c. the x-intercepts d. the square values Explanation This equation is in intercept form: y = a ( x - p )( x - q ). In this case to get the x-intercepts you set (x + 5) and (x + 9) equal to zero. x + 5 = 0 x = - 5 x + 9 = 0 x = - 9 Therefore, x = - 5 and x = - 9 are the x-intercepts. In this case, x = 5 and x = 9 are not the x-intercepts. not the x-intercept Which of the following equations will be the graph of a parabola? a. y = 2x + 4 b. y = x^2 - 2x + 3 c. y = 2x + 3 d. x = y^2 +2x - 3 Here, y = x^2 - 2x + 3 will result in the graph of a parabola because it takes the form of y = ax^2 +bx + c, or a quadratic equation. y = x^2 - 2x + 3 Which one of the following divides the parabola into two equal halves?
- Point of symmetry
- Axis of equality
- Point of equality
- Axis of symmetry The axis of symmetry is the half of the parabola between the minimum and maximum points on a graph. Axis of symmetry
Standard The following equation is written in which parabolic form? y = - ( x - 3)2 - 1 Parenthetical Vertex Standard Intercept Vertex form is set up as: y = a(x - h)2 + k Vertex Which of the following graphs represents the equation, y = - 2x2 + 2x + 6? The correct option is the only graph where the line follows a 'U' shape, making it a parabola. The correct option is the only graph where the line follows a 'U' shape, making it a parabola.
