QQuestionOther Subjects
QuestionOther Subjects
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
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Answer
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Step 1: Find the quadratic equation given the x-intercepts
Since the graph of the function $h(x)$ intersects the x-axis at the points $(0, 0)$ and $(1, 0)$, we can find the quadratic equation using the x-intercepts formula: $h(x) = k(x-x_1)(x-x_2)$, where $x_1$ and $x_2$ are the x-intercepts and $k$ is a constant.
Step 2: Plug in the given x-intercepts
Plug in the given x-intercepts, $(0, 0)$ and $(1, 0)$, into the formula: $h(x) = k(x-0)(x-1)$.
Final Answer
The value of $t$ is 8 (option D).
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