8 Fill in the Blank 1 point Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. Vertex (1,2) Passes through $$ (3,10) $$ $$ y= $$ type your answer...

Question

UpStudy AI · Accepted Answer

To write a quadratic function in vertex form, we use the formula:

$$
y = a(x - h)^2 + k
$$

where $$(h, k)$$ is the vertex of the parabola. In this case, the vertex is $$(1, 2)$$, so we have:

$$
y = a(x - 1)^2 + 2
$$

Next, we need to find the value of $$a$$ using the point $$(3, 10)$$ that the graph passes through. We can substitute $$x = 3$$ and $$y = 10$$ into the equation to solve for $$a$$:

$$
10 = a(3 - 1)^2 + 2
$$

Now, let's simplify and solve for $$a$$:

1. Calculate $$(3 - 1)^2$$:
   $$
   (3 - 1)^2 = 2^2 = 4
   $$

2. Substitute back into the equation:
   $$
   10 = 4a + 2
   $$

3. Subtract 2 from both sides:
   $$
   8 = 4a
   $$

4. Divide by 4:
   $$
   a = 2
   $$

Now that we have $$a$$, we can write the complete quadratic function:

$$
y = 2(x - 1)^2 + 2
$$

Thus, the quadratic function in vertex form is:

$$
y = 2(x - 1)^2 + 2
$$
$$ y = 2(x - 1)^2 + 2 $$

8 Fill in the Blank 1 point Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. Vertex (1,2) Passes through \( (3,10) \) \( y= \) type your answer...

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions