# Chapter 9 - Quadratic Functions and Equations - 9-1 Quadratic Graphs and Their Properties - Practice and Problem-Solving Exercises - Page 539: 42

Vertex: (0,5) Axis of symmetry: x=0

#### Work Step by Step

Given the function $y= -1.5x^{2} + 5$ We need to find the vertex and axis of symmetry The basic form of the equation is $y=a(k(x-d))^{2} + c$ Vertex: The vertex for the base function $y= x^{2}$ is (0,0). Since the d value is zero, the graph does not shift left or right thus the x value of the vertex is 0. Since the c value is 5, the graph moves 5 units up thus the y value of the vertex is 5. Therefore the vertex is (0,5) Axis of symmetry: The Axis of symmetry of a $y= x^{2}$ graph is x=0. Since the d value is zero, the graph does not shift left or right thus the axis of symmetry is still x=0.

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