Write equation in translation form.
$$
f(4)=6
$$

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the vertex form of a parabola. The vertex form of a parabola is given by $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. ‖ ‖ step 2 ⋮ Given the vertex $(1, -2)$, we substitute $h = 1$ and $k = -2$ into the vertex form: $y = a(x - 1)^2 - 2$. ‖ ‖ step 3 ⋮ Use the y-intercept $(0, 0)$ to find $a$. Substitute $x = 0$ and $y = 0$ into the equation: $0 = a(0 - 1)^2 - 2$. ‖ ‖ step 4 ⋮ Solve for $a$: $0 = a(1) - 2 \implies a = 2$. ‖ ‖ step 5 ⋮ Substitute $a = 2$ back into the vertex form: $y = 2(x - 1)^2 - 2$. ‖ ‖ step 6 ⋮ Verify the x-intercepts $(-2, 0)$ and $(3, 0)$ by solving $0 = 2(x - 1)^2 - 2$. ‖ ‖ step 7 ⋮ Solve $0 = 2(x - 1)^2 - 2$: $2(x - 1)^2 = 2 \implies (x - 1)^2 = 1 \implies x - 1 = \pm 1 \implies x = 2 \pm 1 \implies x = -2 ext{ or } x = 3$. ‖ ‖ step 8 ⋮ Confirm the function value $f(4) = 6$ by substituting $x = 4$ into the equation: $f(4) = 2(4 - 1)^2 - 2 = 2(3)^2 - 2 = 2(9) - 2 = 18 - 2 = 16$. ‖ ∻Answer∻ ⚹ The equation of the parabola in translation form is $y = 2(x - 1)^2 - 2$. ⚹ ∻Key Concept∻ ⚹Vertex form of a parabola⚹ ∻Explanation∻ ⚹The vertex form of a parabola is useful for identifying the vertex and transforming the equation to match given points.⚹◊What is the standard form of the equation for a parabola that opens upwards?⍭ Generate me a similar question◊

Sia