Maths-
General
Easy
Question
Graph f(x) = x2 + 2x + 4. What are axis of symmetry, vertex and y-intercept of the function
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 y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
The correct answer is: 4
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)=x2+2x+4, a=1, b=2, and c=4. So, the equation for the axis of symmetry is given by
X = −(2)/2(1)
x = - 2/2
x = -1
The equation of the axis of symmetry for f(x)=x2+2x+4 is x = -1.
The x coordinate of the vertex is the same:
h = -1
The y coordinate of the vertex is :
k = f(h)
k = (h)2 + 2(h) + 4
k = (-1)2 + 2(-1) + 4
k = 1 – 2 + 4
k = 3
Therefore, the vertex is (-1 , 3)
For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.
y = (0)2 + 2(0) + 4
y = 0 + 0 + 4
y = 4
Therefore, Axis of symmetry is x = -1
Vertex is ( -1 , 3 )
Y- intercept is 4.
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