Question

1. find the axis of symmetry and vertex of $-4 + x^2 = -3x$ by graphing.

axis of symmetry:
vertex:

Explanation:

Step1: Rewrite the equation

First, rewrite the given equation \(-4 + x^2 = -3x\) in standard quadratic form \(y = ax^2 + bx + c\). Rearranging terms, we get \(y = x^2 + 3x - 4\).

Step2: Find the axis of symmetry

The formula for the axis of symmetry of a quadratic function \(y = ax^2 + bx + c\) is \(x = -\frac{b}{2a}\). For \(y = x^2 + 3x - 4\), \(a = 1\) and \(b = 3\). Plugging these values into the formula, we have \(x = -\frac{3}{2(1)} = -\frac{3}{2} = -1.5\).

Step3: Find the vertex

The x-coordinate of the vertex is the same as the axis of symmetry, so \(x = -1.5\). To find the y-coordinate, substitute \(x = -1.5\) into the quadratic function:

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So the vertex is \((-1.5, -6.25)\).

Answer:

Axis of symmetry: \(x = -1.5\)
Vertex: \((-1.5, -6.25)\)