How do you solve #0 = x^2 + 4x + 4 # graphically and algebraically?

Question

Eli Assouline · Accepted Answer

#x = -2#

Algebraically, factorize and solve for each factor that equals zero.

#(x+2)(x+2) = 0#

#x+2 = 0 rArr x =-2" both give the same answer"#

Graphically: Draw the graph of #color(blue)(y) = x^2 +4x +4# This will be a parabola.

To solve #x^2 +4x+4 = color(blue)(0)# , read the point(s) from the graph where the parabola cuts the #x#-axis.

The # x#-axis is the line where # color(blue)(y=0)#

The parabola will intersect (touch) at only point where #x = -2#graph{x^2+4x+4 [-10, 10, -5, 5]}

Isaiah Anthony · Answer

undefined To solve the equation $0 = x^2 + 4x + 4$ graphically, you can plot the graph of the quadratic function $y = x^2 + 4x + 4$ and identify the x-intercepts, which represent the solutions to the equation.

To solve the equation algebraically, you can use the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$, where $a = 1$, $b = 4$, and $c = 4$. Plug these values into the formula and calculate the solutions.

Eva Adamson · Answer

undefined To solve the equation $0 = x^2 + 4x + 4$ graphically, you can plot the quadratic function $y = x^2 + 4x + 4$ on a coordinate plane and identify the points where the graph intersects the x-axis. These points represent the solutions to the equation. In this case, since the equation is a perfect square trinomial, the graph will touch the x-axis at a single point, indicating that there is one real solution.

Algebraically, you can solve the equation by using the quadratic formula, which states that for a quadratic equation $ax^2 + bx + c = 0$, the solutions are given by:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

For the equation $0 = x^2 + 4x + 4$, identify $a$, $b$, and $c$ as follows:

$$a = 1$$
$$b = 4$$
$$c = 4$$

Substitute these values into the quadratic formula:

$$x = \frac{-4 \pm \sqrt{4^2 - 4(1)(4)}}{2(1)}$$

$$x = \frac{-4 \pm \sqrt{16 - 16}}{2}$$

$$x = \frac{-4 \pm \sqrt{0}}{2}$$

Since the discriminant ($b^2 - 4ac$) is zero, the quadratic formula simplifies to:

$$x = \frac{-4}{2}$$

$$x = -2$$

Thus, the algebraic solution to the equation $0 = x^2 + 4x + 4$ is $x = -2$. This confirms that there is one real solution, as observed graphically.