Solve y=2-x^2 - Socratic AI (ScanMath)

Pertanyaan

Function

Find the vertex

Find the axis of symmetry

Evaluate the derivative

Muat lebih banyak

(0, 2)

Evaluate

y = 2 - x^{2}

Write the quadratic function in standard form

y = - x^{2} + 2

Find the x -coordinate of the vertex by substituting a= - 1 and b= 0 into x = - \frac{b}{2 a}

x = - \frac{0}{2 ( - 1 )}

Solve the equation for x

x = 0

Find the y-coordinate of the vertex by evaluating the function for x = 0

y = - 0^{2} + 2

Calculate

Langkah Lebih Banyak

Evaluate

- 0^{2} + 2

Calculate

- 0 + 2

Simplify

0 + 2

Removing 0 doesn't change the value,so remove it from the expression

2

y = 2

Larutan

(0, 2)

Tampilkan Solusi

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Tidak simetris terhadap titik asal.

Evaluate

y = 2 - x^{2}

To test if the graph of y = 2 - x^{2} is symmetry with respect to the origin,substitute -x for x and -y for y

- y = 2 - (- x)^{2}

Simplify

- y = 2 - x^{2}

Change the signs both sides

y = - 2 + x^{2}

Larutan

Tidak simetris terhadap titik asal.

Tampilkan Solusi

Identify the conic

Find the standard equation of the parabola

Find the vertex of the parabola

Find the focus of the parabola

Muat lebih banyak

x^{2} = - (y - 2)

Evaluate

y = 2 - x^{2}

Swap the sides of the equation

2 - x^{2} = y

Move the constant to the right-hand side and change its sign

- x^{2} = y - 2

Multiply both sides of the equation by - 1

- x^{2} (- 1) = (y - 2) (- 1)

Multiplying or dividing an even number of negative terms equals a positive

x^{2} = (y - 2) (- 1)

Multiply the terms

Langkah Lebih Banyak

Evaluate

(y - 2) (- 1)

Apply the distributive property

y (- 1) - 2 (- 1)

Multiplying or dividing an odd number of negative terms equals a negative

- y - 2 (- 1)

Simplify

- y + 2

x^{2} = - y + 2

Larutan

x^{2} = - (y - 2)

Tampilkan Solusi

Solve the equation

x = - y + 2 x = - - y + 2

Evaluate

y = 2 - x^{2}

Swap the sides of the equation

2 - x^{2} = y

Move the constant to the right-hand side and change its sign

- x^{2} = y - 2

Change the signs on both sides of the equation

x^{2} = - y + 2

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm - y + 2

Larutan

x = - y + 2 x = - - y + 2

Tampilkan Solusi

Rewrite the equation

r = \frac{- sin ( θ ) + 7 cos ^{2} ( θ ) + 9}{2 cos ^{2} ( θ )} r = - \frac{sin ( θ ) + 7 cos ^{2} ( θ ) + 9}{2 cos ^{2} ( θ )}

Evaluate

y = 2 - x^{2}

Move the expression to the left side

y + x^{2} = 2

To convert the equation to polar coordinates,substitute r cos (θ) for x and r sin (θ) for y

sin (θ) \times r + (cos (θ) \times r)^{2} = 2

Factor the expression

cos^{2} (θ) \times r^{2} + sin (θ) \times r = 2

Subtract the terms

cos^{2} (θ) \times r^{2} + sin (θ) \times r - 2 = 2 - 2

Evaluate

cos^{2} (θ) \times r^{2} + sin (θ) \times r - 2 = 0

Solve using the quadratic formula

r = \frac{- sin ( θ ) \pm sin ^{2} ( θ ) - 4 cos ^{2} ( θ ) ( - 2 )}{2 cos ^{2} ( θ )}

Simplify

r = \frac{- sin ( θ ) \pm 7 cos ^{2} ( θ ) + 9}{2 cos ^{2} ( θ )}

Separate the equation into 2 possible cases

r = \frac{- sin ( θ ) + 7 cos ^{2} ( θ ) + 9}{2 cos ^{2} ( θ )} r = \frac{- sin ( θ ) - 7 cos ^{2} ( θ ) + 9}{2 cos ^{2} ( θ )}

Larutan

r = \frac{- sin ( θ ) + 7 cos ^{2} ( θ ) + 9}{2 cos ^{2} ( θ )} r = - \frac{sin ( θ ) + 7 cos ^{2} ( θ ) + 9}{2 cos ^{2} ( θ )}

Tampilkan Solusi

Grafik

Y=2 X^2

Function

Testing for symmetry

Identify the conic

Solve the equation

Rewrite the equation

Grafik