Question

For Problems 1 and 2, show all necessary work. Identify the values you were give substituted them into the vertex form of the equation. y=a(x-h)^(2)+k Write the vertex form for the quadratic function

Answer 1

In a quadratic function, the vertex form is represented as y = a(x - h)² + k, where (h, k) is the vertex of the parabola, and 'a' determines the direction and steepness of the parabola. In this case, we have been given values of a, h, and k as 1, 0, and 0 respectively.

Step 1: Substitute the given values into the vertex form of the equation.

Replace 'a' with 1, 'h' with 0, and 'k' with 0 in the equation. So, the equation will be y = 1(x - 0)² + 0.

y = (1 · (x - 0) ^ 2) + 0

Step 2: Simplify the equation.

Next, since anything minus zero remains the same, we simplify the equation to be: y = (1 · x ^ 2) + 0

Step 3: Apply the identity.

1 times anything remains the same, as well, so the equation becomes: y = x². And adding zero to anything does not change its value. Therefore, we get our final equation: y = x².

So, the vertex form for the given quadratic function is y = x².