write this equation in standard form.
y=1/2x2+12x-8
y equals one half x squared plus 12x minus 8
To write the given equation, y = (1/2)x^2 + 12x - 8, in standard form, you need to rearrange the terms so that the equation is in the form: Ax^2 + Bx + C = 0, where A, B, and C are constants.
Step 1: Multiply through by 2 to eliminate the fraction:
2y = x^2 + 24x - 16
Step 2: Move all the terms to one side to have 0 on the other side:
x^2 + 24x - 16 - 2y = 0
In this form, the equation is now written in standard form: x^2 + 24x - 2y - 16 = 0.
To write the equation in standard form, we need to get rid of the fraction. Let's multiply the entire equation by 2 to clear the fraction:
2y = 2 * (1/2)x^2 + 2 * 12x - 2 * 8
This simplifies to:
2y = x^2 + 24x - 16
Now, let's move all the terms to one side to obtain the equation in standard form:
x^2 + 24x - 2y - 16 = 0
So, the equation in standard form is:
x^2 + 24x - 2y - 16 = 0