Question

Transform the given quadratic function in the form of

y =a*x²+bx+c into y=a*(x-h)²+k
y =7x²-2x+1
h =
k =
y =
Vertex =

Answer 1

The quadratic function y = 7x² - 2x + 1 can be transformed into vertex form y = 7(x - 1/7)² + 1/7 with the vertex of the parabola being (1/7, 1/7).

Step-by-step explanation:

The question involves transforming a quadratic function from the standard form y = ax² + bx + c to the vertex form y = a(x - h)² + k.

In this case, the given quadratic function is y = 7x² - 2x + 1. To convert it to vertex form, we follow these steps:

1. Find the vertex (h, k) of the parabola. The vertex can be found using the formula h = -b/2a and then finding k by plugging h back into the original equation.
2. Once the vertex is found, rewrite the function in vertex form using the values of h and k.

First, let's find h:
h = -(-2)/(2*7)

= 1/7
Next, we calculate k by substituting h back into the function:
k = 7(1/7)² - 2(1/7) + 1

= 7/49 - 2/7 + 1

= 1/7
Finally, we write the vertex form with the found values:
y = 7(x - 1/7)² + 1/7

The vertex of the parabola in this case is (1/7, 1/7).