Aug 5, 2019 · Axis of Symmetry: The parabola is symmetric about the y-axis, meaning if you fold the graph along the y-axis, both sides will match. Domain: The domain of y = x 2 is all real numbers, denoted as (− ∞, ∞), since you can input any value for x. Range: The range of y = x 2 includes all non-negative values, expressed as [0, ∞).

Jan 21, 2020 · x = y 2 − 7. Step-by-step explanation: We have been given an equation y = x 2 − 7. We are asked to determine that which equation can be simplified to find the inverse of our given equation. We know that to find inverse of an equation, the x and y-values are interchanged. Let us interchange x and y values for our given equation. x = y 2 − 7

The roots of the function y = x2 + 2x - 3 are 1 and -3, found by solving for x using the quadratic formula. The turning point or vertex of the function is at (-1, -4), determined using the formula -b / 2a. Explanation: The given function is a quadratic function, written in standard form, which is y = ax2 + bx + c. Here, 'a' is the coefficient ...

Oct 12, 2023 · y = − ∣ x − 2∣. y = x 2 + 2. Calculation Steps: Graph the quadratic equation y = x 2 + 2, which will be a parabola opening upwards with vertex at (0, 2). Graph the absolute value equation y = − ∣ x − 2∣, which will be a V-shaped graph that is inverted (opening downwards) with the vertex at (2, 0).

Oct 31, 2017 · To find the inverse of the function given by the equation y = x 2 − 36, we will start by swapping the roles of x and y in the equation. Here are the steps to follow: Replace y with x: x = y 2 − 36. Rearrange to isolate y: Add 36 to both sides: x + 36 = y 2. Take the square root: y = ± x + 36 This means the inverse function can be expressed ...

Feb 8, 2018 · The given function is ⇒⇒⇒ y = x² + 4x + 4 To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i.e. make x as y and y as x) y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation y = (x+2)(x+2) y = (x+2)² ⇒⇒⇒ take the square root to both sides √y = x+2 x = √y - 2 ⇒⇒⇒ x becomes a function of y ...

So we can rewrite the equation as: y = (x 2 − 6 x + 9) − 9 + 18 This simplifies to: y = (x − 3) 2 + 9. Vertex form: Now we have the equation in vertex form, which is y = a (x − h) 2 + k where (h, k) is the vertex. From our final equation, we can see that the vertex is at (3, 9). Thus, the vertex form of the given quadratic equation is ...

y = x 2 − 3 x + 7 y = 3 x − 2. Since both equations equal y, we can set them equal to each other to find the value of x: x 2 − 3 x + 7 = 3 x − 2. Next, we will rearrange the equation: x 2 − 3 x − 3 x + 7 + 2 = 0 x 2 − 6 x + 9 = 0 (x − 3) 2 = 0. This implies that: x = 3. Now we substitute the value of x back into either equation ...

Mar 15, 2022 · Now we will find the corresponding y values for each x: For x = − 4: y = (− 4) 2 − 4 = 16 − 4 = 12 So, one solution is (− 4, 12). For x = 3: y = (3) 2 − 4 = 9 − 4 = 5 So, another solution is (3, 5). The solutions to the system of equations are (3, 5) and (− 4, 12). Comparing with the options provided, the correct answer is A. (3 ...

Dec 30, 2020 · To correctly find the inverse, starting from x = y 2 + 12 y, we would rearrange it to: y 2 + 12 y − x = 0 and apply the quadratic formula: y = 2 − 12 ± 1 2 2 + 4 x = − 6 ± 36 + x . From here, we focus on the positive root to ensure we're adhering to the convention of inverse functions, especially since we're considering x ≥ − 6 .