Graph the following quadratic function. First state the vertex, Iine of symmetry, y-intercept, and xintercepts. All values should be exact. Your graph must have at least three labelled points, one of which must be the vertex. f(x)=1/4 x^2+x-3

FizeauV

FizeauV

Answered question

2021-05-27

Graph the following quadratic function. First state the vertex, Iine of symmetry, y-intercept, and xintercepts. All values should be exact. Your graph must have at least three labelled points, one of which must be the vertex. f(x)=14x2+x3

Answer & Explanation

Bertha Stark

Bertha Stark

Skilled2021-05-28Added 96 answers

The xx-coordinate of the vertex of y=ax^2+bx+c. From the given, we have a=14, b=1, and c=−3 so: x=(12(14))=2
The y-coordinate of the vertex (using the function) is: y=14(2)2+(2)3=4
So, the vertex is at (−2,−4).
The line of symmetry of y=ax2+bx+c is x=−b2a (same as the xx-coordinate of the vertex and is a vertical line) so:
x=−2
To find the y-intercept, set x=0 and solve for y using the given function:
y=14(0)2+0−3=−3
So, the y-intercept is at (0,−3).
To find the x-intercepts, set y=0 and solve for xx using the given function:
0=14x2+x3
Factor the right side:
0=14(x2+4x12)
0=14(x2)(x+6)
By zero product property,
x=−6,2
So, the xx-intercepts are at (−6,0) and (2,0).
The graph will be:
[Graph]

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