Question

Standard form of y= -2(x - 4)^2+18

Answer 1

To convert the given quadratic equation y = -2(x - 4)^2+18 into standard form, expand and rearrange it as 0 = 2x^2 - 16x + 14.

Step-by-step explanation:

The student has presented an equation y = -2(x - 4)^2+18 and asks to convert it into standard form. The standard form of a quadratic equation is expressed as ax^2 + bx + c = 0. To put the given equation in standard form, we expand and rearrange the given quadratic expression in descending powers of x.

Expanding the equation gives:

• y = -2(x^2 - 8x + 16) + 18
• y = -2x^2 + 16x - 32 + 18
• y = -2x^2 + 16x - 14

To convert to standard form, rearange it as:

• 0 = 2x^2 - 16x + 14

Finally, we have the standard form of the quadratic equation:

• 0 = 2x^2 - 16x + 14