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ankoles [38]
2 years ago
13

Find the vertex, axis of symmetry, and y-intercept of the quadratic function.

Mathematics
2 answers:
Ostrovityanka [42]2 years ago
6 0

Answer:

Below in bold.

Step-by-step explanation:

f(x) = 1/2x^2 + 4x

Convert to vertex form:

f(x) = 1/2(x^2 + 8x)

= 1/2 [(x + 4)^2 - 16]

= 1/2(x + 4)^2 - 8    <------ Vertex form.

So the Vertex is at (-4, - 8).

Axis of symmetry is x = -4.

y -intercept (when x = 0) =  8-8 = 0.

Vlada [557]2 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then

the x- coordinate of the vertex is

x_{vertex} = - \frac{b}{2a}

f(x) = \frac{1}{2} x² + 4x ← is in standard form

with a = \frac{1}{2} , b = 4 , c = 0 , then

x_{vertex} = - \frac{4}{1} = - 4

substitute x = - 4 into f(x) for corresponding y- coordinate of vertex

f(- 4) = \frac{1}{2} (- 4)² + 4(- 4) = \frac{1}{2} × 16 - 16 = 8 - 16 = - 8

vertex = (- 4, - 8 )

the equation of the axis of symmetry is a vertical line passing through the vertex with equation

x = c ( c is the x- coordinate of the vertex ) , then equation of axis of symmetry is

x = - 4

to find the y- intercept substitute x = 0 into f(x)

f(0) = \frac{1}{2} (0)² + 4(0) = 0 + 0 = 0

then y- intercept is 0

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