Questions: Identify the vertex and x - and y-intercepts.

Identify the vertex and x - and y-intercepts.
Transcript text: Question 1 1 pts Identify the vertex and $x$ - and $y$-intercepts.
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Solution

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Solution Steps

Step 1: Find the vertex.

The given quadratic function is in the form f(x) = ax² + bx + c, where a = -1, b = -4, and c = -3. The x-coordinate of the vertex is given by x = -b/2a. x = -(-4) / 2(-1) = 4 / -2 = -2

Substitute x = -2 into the function to find the y-coordinate of the vertex: f(-2) = -(-2)² - 4(-2) - 3 = -4 + 8 - 3 = 1

So, the vertex is (-2, 1).

Step 2: Find the x-intercepts.

To find the x-intercepts, set f(x) = 0 and solve for x: -x² - 4x - 3 = 0 Multiply by -1: x² + 4x + 3 = 0 Factor the quadratic equation: (x + 3)(x + 1) = 0 x = -3 or x = -1 The x-intercepts are (-3, 0) and (-1, 0).

Step 3: Find the y-intercept.

To find the y-intercept, set x = 0: f(0) = -(0)² - 4(0) - 3 = -3 The y-intercept is (0, -3).

Final Answer

Vertex: (-2, 1) x-intercepts: (-3, 0) and (-1, 0) y-intercept: (0, -3)

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