**Step 1:**

X - intercept are:

$$ \begin{aligned} & \color{blue}{ x_1 = -3 } \\[1 em] & \color{blue}{ x_2 = 1 } \end{aligned} $$To find the x-intercepts, we need to solve equation $ x^2+2x-3 = 0 $. (use the quadratic equation solver to view a detailed explanation of how to solve the equation)

**Step 2:**

Y - intercept is point: $ y-inter=\left(0,~-3\right) $

To find y - coordinate of y - intercept, we need to compute $ f(0) $. In this example we have:

$$ f(\color{blue}{0}) = 1 \cdot \color{blue}{0}^2 + 2 \cdot \color{blue}{0} -3 = -3$$**Step 3:**

Vertex is point: $V=\left(-1,~-4\right) $

To find the x - coordinate of the vertex we use formula:

$$ x = -\frac{b}{2a} $$In this example: $ a = 1, b = 2, c = -3 $. So, the x-coordinate of the vertex is:

$$ x = -\frac{b}{2a} = -\frac{ 2 }{ 2 \cdot 1 } = -1 $$$$ y = f \left( -1 \right) = 1 \left( -1 \right)^2 + 2 \cdot \left( -1 \right) ~ - ~ 3 = -4 $$**Step 4:**

Focus is point: $ F=\left(-1,~-\dfrac{ 15 }{ 4 }\right)$

The x - coordinate of the focus is $ x = -\dfrac{b}{2a} $

The y - coordinate of the focus is $ y = \dfrac{1-b^2}{4a} + c $

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