h of x equals, 2 times, open parenthesis, x minus 4, close parenthesis, squared, minus 32

The quadratic fu...

Question

h of x equals, 2 times, open parenthesis, x minus 4, close parenthesis, squared, minus 32

The quadratic function *h* is defined as shown. In the *xy*-plane, the graph of *y* = *h*(*x*) intersects the *x*-axis at the points (0, 0) and (1, 0), where *t* is a constant.

What is the value of *t*?

- A. 1
- B. 2
- C. 4
- D. 8

CramX · Accepted Answer

Step 1: : Find the quadratic equation given the x-intercepts. Step 2: : Plug in the given x-intercepts. Step 3: : Simplify the equation. Step 4: : Compare the simplified equation with the given quadratic function. We can see that the leading coefficient is different, so we need to adjust our equation to match the given one. Step 5: : Find the value of $k$. Step 6: : Plug in the value of $k$ into the simplified equation. Step 7: : Expand the simplified equation. Step 8: : Compare the expanded equation with the given quadratic function. We can see that the linear term is different, so we need to adjust our equation to match the given one. Step 9: : Complete the square for the simplified equation. Step 10: : Simplify the adjusted equation. Step 11: : Compare the simplified adjusted equation with the given quadratic function. We can see that the constant term is different, so we need to adjust our equation to match the given one. Step 12: : Find the value of the constant term. Step 13: : Compare the simplified adjusted equation with the given quadratic function (again). We can see that the constant term is still different, so we need to adjust our equation to match the given one. Step 14: : Find the value of $t$. Final Answer: The value of $t$ is 8 (option D).

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Step 1:
: Find the quadratic equation given the x-intercepts

Step 2:
: Plug in the given x-intercepts

Step 3:
: Simplify the equation

Final Answer

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