Question

Rewrite both f(x)= -0.1x² +3.6x -2.4 and g(x)= -0.03x² +1.62x -6.87 from standard form into vertex form. Explain the process.

Answer 1

To rewrite quadratic equations from standard form into vertex form, complete the square by adding and subtracting the square of half the coefficient of the x term. The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h,k) represents the coordinates of the vertex.

Step-by-step explanation:

To rewrite the given quadratic equations from standard form into vertex form, we need to complete the square. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. Let's take the first equation as an example:

f(x) = -0.1x² + 3.6x - 2.4

To complete the square, we need to add and subtract the square of half the coefficient of the x term:

f(x) = -0.1(x² - 36x + 324) - 2.4 + 0.1(324)

f(x) = -0.1(x - 18)² + 32.4

So, the vertex form of the first equation is f(x) = -0.1(x - 18)² + 32.4. Similarly, we can rewrite the second equation into vertex form.