Solve by graphing
1. 2x2-7x+5=0
2. 2x2+x-6=0
To solve these quadratic equations by graphing, you can follow these steps:
1. Start by rewriting the equations in the standard form: ax^2 + bx + c = 0.
Equation 1: 2x^2 - 7x + 5 = 0
Equation 2: 2x^2 + x - 6 = 0
2. To graph these equations, plot points on a coordinate plane. Remember that a quadratic equation represents a parabola.
3. Find the y-intercept: Plug in x = 0 into each equation to find the y-intercept.
For Equation 1: When x = 0, 2(0)^2 - 7(0) + 5 = 5. So the y-intercept is (0, 5).
For Equation 2: When x = 0, 2(0)^2 + (0) - 6 = -6. So the y-intercept is (0, -6).
4. Find the x-intercepts: Set the equation equal to zero (y = 0) and solve for x. These are the points where the graph intersects the x-axis.
For Equation 1, solve 2x^2 - 7x + 5 = 0 for x. You can use factoring, quadratic formula, or completing the square to solve the equation. Let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values for Equation 1: a = 2, b = -7, c = 5, x = (-(-7) ± √((-7)^2 - 4(2)(5))) / (2(2)).
Simplifying gives us x = (7 ± √(49 - 40)) / 4.
Simplifying further gives us x = (7 ± √9) / 4.
x = (7 ± 3) / 4.
So the x-intercepts are x = 5/2 and x = 1.
For Equation 2, solve 2x^2 + x - 6 = 0 for x using the same steps. You will find the x-intercepts at x = -3/2 and x = 2.
5. Plot the y-intercept and x-intercepts on the graph.
6. Draw a smooth curve that passes through all these points. This represents the graph of the quadratic equation.
By visually analyzing the graph, you can determine the approximate values of x for which the equation equals zero. These values represent the solutions to the equations.
Please note that if the graph doesn't intersect the x-axis, it means there are no real solutions.
Now, you can follow these steps to solve both equations by graphing.