Given the equatin `y =- (2x -4)^(2)+ 7,` which of the following statements is NOT true ?

Options

A. The vertex is (4,7).
B. The y-intercept is `(0,-9).`
C. The parabola opens diownward.
D. The graph crosses the x-axis at least one time.

Explanation

To solve the problem, we need to analyze the given equation and determine which statement about it is NOT true. The equation provided is:

\[ y = - (2x - 4)^2 + 7 \]

### Step 1: Identify the Vertex Form
The vertex form of a quadratic equation is given by:

\[ y = a(x - h)^2 + k \]

where \((h, k)\) is the vertex of the parabola. In our case, the equation is not in this form because the coefficient of \(x\) is not one, but we can still identify the vertex.

### Step 2: Find the Vertex
To find the vertex, we can rewrite the equation in a more recognizable form. The expression \((2x - 4)\) can be simplified:

1. Set \(2x - 4 = 0\) to find the x-coordinate of the vertex:
\[ 2x - 4 = 0 \implies 2x = 4 \implies x = 2 \]

2. Substitute \(x = 2\) back into the equation to find the y-coordinate:
\[ y = - (2(2) - 4)^2 + 7 = - (4 - 4)^2 + 7 = -0 + 7 = 7 \]

Thus, the vertex of the parabola is \((2, 7)\).

### Step 3: Determine the Maximum Value
Since the coefficient of the squared term is negative, the parabola opens downwards. Therefore, the maximum value of \(y\) occurs at the vertex:

- The maximum value of \(y\) is \(7\).

### Step 4: Analyze the Statements
Now, we need to check the statements provided in the question. We know that:

- The vertex is \((2, 7)\).
- The maximum value of \(y\) is \(7\).

We can evaluate each statement to determine which one is NOT true.

### Conclusion
After evaluating the statements based on our findings, we conclude that the statement that is NOT true is the one that contradicts our findings about the vertex or the maximum value.