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docker41 [41]
3 years ago
11

The graph of the function y=x^2-x-2 is shown below

Mathematics
2 answers:
Natali5045456 [20]3 years ago
8 0

Answer:

Option D is correct

Step-by-step explanation:

A quadratic equation is in the form of y =ax^2+bx+c   ....[1]

then;

the axis of symmetry is given by:

x = \frac{-b}{2a}

Vertex = (\frac{-b}{2a}, f(\frac{-b}{2a})

As per the statement:

Given the function:

y=f(x) =x^2-x-2        ....[2]

On comparing with [1] we have;

a = 1, b = -1 and c = -2

Then;

x =\frac{-(-1)}{2(1)} = \frac{1}{2}

Substitute the value of x in f(x) we have;

f(\frac{1}{2}) = (\frac{1}{2})^2-\frac{1}{2}-2 = \frac{1}{4}-\frac{5}{2} = \frac{1-10}{4} = \frac{-9}{4}

⇒f(\frac{1}{2}) = -2\frac{1}{4}

Vertex =(\frac{1}{2}, -2\frac{1}{4})

x-intercept states that the graph crosses the x-axis.

From the graph, the function cuts the x-axis at:

x = -1 and x = 2

x-intercepts = (-1, 0) and (2, 0)

y-intercept states that the graph crosses the y-axis

From the given graph we have;

y = -2

y-intercept = (0, -2)

Therefore,

Vertex =(\frac{1}{2}, -2\frac{1}{4})

Axis of symmetry: x=\frac{1}{2}

x-intercepts = (-1, 0) and (2, 0)

y-intercept = (0, -2)

Zinaida [17]3 years ago
7 0
The answer to this quistion is D
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