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Maths-

General

Easy

Question

Estimate the coordinates of the vertex of the graph of f(x) = 1.25x² -2x -1 below. Then explain how to find the exact coordinates

hint Hint:

For a quadratic function is in standard form, f(x)=ax2+bx+c.
A vertical line passing through the vertex is called the axis of symmetry for the parabola.
Axis of symmetry x=−b/2a
Vertex The vertex of the parabola is located at a pair of coordinates which we will call (h, k). where h is value of x in axis of symmetry formula and k is f(h).

The correct answer is: (0.8 , -1.8)

We have given a function
f(x) = 1.25x² -2x -1
This quadratic function is in standard form, f(x)=ax²+bx+c.
For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
In f(x)= 1.25x² -2x -1, a= 1.25, b= -2, and c= -1. So, the equation for the axis of symmetry is given by
x = −(-2)/2(1.25)
x = 2/2.5
x = 0.8
The equation of the axis of symmetry for f(x)= 1.25x² -2x -1 is x = 0.8.
The x coordinate of the vertex is the same:
h = 0.8
The y coordinate of the vertex is :
k = f(h)
k = 1.25h² -2h -1
k = 1.25(0.8)² - 2(0.8) - 1
k = 0.8 - 1.6 – 1
k = -1.8
Therefore, the vertex is (0.8 , -1.8)

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