Solve b= -4x^2 - 6x -4

Question

Function

Find the vertex

Find the axis of symmetry

Rewrite in vertex form

(- \frac{3}{4}, - \frac{7}{4})

Show Solution

x = \frac{- 3 + - 7 - 4 b}{4} x = - \frac{3 + - 7 - 4 b}{4}

Evaluate

b = - 4 x^{2} - 6 x - 4

Swap the sides of the equation

- 4 x^{2} - 6 x - 4 = b

Move the expression to the left side

- 4 x^{2} - 6 x - 4 - b = 0

Multiply both sides

4 x^{2} + 6 x + 4 + b = 0

Substitute a= 4,b= 6 and c= 4 + b into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 6 \pm 6 ^{2} - 4 \times 4 ( 4 + b )}{2 \times 4}

Simplify the expression

x = \frac{- 6 \pm 6 ^{2} - 4 \times 4 ( 4 + b )}{8}

Simplify the expression

More Steps

x = \frac{- 6 \pm - 28 - 16 b}{8}

Simplify the radical expression

More Steps

x = \frac{- 6 \pm 2 - 7 - 4 b}{8}

Separate the equation into 2 possible cases

x = \frac{- 6 + 2 - 7 - 4 b}{8} x = \frac{- 6 - 2 - 7 - 4 b}{8}

Simplify the expression

More Steps

x = \frac{- 3 + - 7 - 4 b}{4} x = \frac{- 6 - 2 - 7 - 4 b}{8}

Solution

More Steps

x = \frac{- 3 + - 7 - 4 b}{4} x = - \frac{3 + - 7 - 4 b}{4}

Show Solution