y=2x^2+5x-3
a)determine the x-intercepts
b)determine the vertex
c)determine the axis of symmetry
d)determine the maximum or minimum value, stating whether it is a maximum or a minimum
e)determine the range
can i get the equations so i can try them myself?
For a and b, there is some solving to do.
For the y intercepts, put x=0 in the equation given and solve for y. For the x intercepts, put y=0 in the equation and solve for x with the quadratic equation.
You will have to do some factoring on the equation to put it in standard form.
See
http://www.analyzemath.com/parabola/Equation.html
Sure! Here are the equations you can use to solve each part of the problem:
a) To determine the x-intercepts, plug in y = 0 into the equation and solve for x using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). In this case, plug in 0 for y, a = 2, b = 5, and c = -3. Solve for x to find the x-intercepts.
b) To determine the vertex, use the formula x = -b / (2a) to find the x-coordinate of the vertex. In this case, a = 2 and b = 5. Plug in these values to find the x-coordinate. Then, substitute this value back into the equation to find the corresponding y-coordinate.
c) The axis of symmetry is a vertical line that passes through the vertex of the parabola. Use the formula x = -b / (2a) calculated in part b to determine the equation for the axis of symmetry.
d) To determine the maximum or minimum value, you need to analyze the coefficient of x^2 (a). If a is positive, the parabola opens upwards and the vertex is the minimum point. If a is negative, the parabola opens downwards and the vertex is the maximum point.
e) To determine the range, you need to find the minimum or maximum value obtained from part d and determine whether the range is all real numbers greater than or equal to the minimum value (for a minimum) or all real numbers less than or equal to the maximum value (for a maximum).
I hope this helps! Let me know if you have any further questions.