1) f (x) = x² + 8x + 202) f (x) = 2x² − 4x + 4-ano ang sagot?​

Answer:1. (−4,4)2.Step-by-step explanation:Find the vertex: The vertex form of a quadratic function is useful for identifying the maximum or minimum point. For a quadratic function in standard form 2++ax 2 +bx+c, the vertex (ℎ,)(h,k) can be found using:ℎ=−2h=− 2ab​ =(ℎ)k=f(h)For your function ()=2+8+20f(x)=x 2 +8x+20:Here, =1a=1, =8b=8, and =20c=20.Calculate ℎh:ℎ=−82⋅1=−4h=− 2⋅18​ =−4Substitute =−4x=−4 back into the function to find k:=(−4)=(−4)2+8(−4)+20=16−32+20=4k=f(−4)=(−4) 2 +8(−4)+20=16−32+20=4So, the vertex of the parabola is (−4,4)(−4,4).Determine the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex, so it is =−4x=−4.Find the y-intercept: This is where the graph crosses the y-axis (when =0x=0):(0)=02+8(0)+20=20f(0)=0 2 +8(0)+20=20So, the y-intercept is (0,20)(0,20).Find the x-intercepts (if any): To find the x-intercepts, solve ()=0f(x)=0:2+8+20=0x 2 +8x+20=0Use the quadratic formula =−±2−42x= 2a−b± b 2 −4ac​ ​ :Here, =1a=1, =8b=8, and =20c=20.Compute the discriminant:Δ=2−4=82−4⋅1⋅20=64−80=−16Δ=b 2 −4ac=8 2 −4⋅1⋅20=64−80=−16Since the discriminant is negative, there are no real x-intercepts; the parabola does not cross the x-axis.So the function represents a parabola that opens upwards, with its vertex at (−4,4)(−4,4), and does not intersect the x-axis.Vertex: To find the vertex, use the formula for ℎh (the x-coordinate of the vertex):ℎ=−2h=− 2ab​ Here, =2a=2, =−4b=−4, and =4c=4:ℎ=−−42⋅2=44=1h=− 2⋅2−4​ = 44​ =1To find the k (the y-coordinate of the vertex), substitute =1x=1 into the function:=(1)=2(1)2−4(1)+4=2−4+4=2k=f(1)=2(1) 2 −4(1)+4=2−4+4=2So, the vertex of the parabola is (1,2)(1,2).Axis of Symmetry: This is the vertical line that passes through the vertex, which is =1x=1.Y-Intercept: The y-intercept is found by setting =0x=0:(0)=2(0)2−4(0)+4=4f(0)=2(0) 2 −4(0)+4=4So, the y-intercept is (0,4)(0,4).X-Intercepts: To find the x-intercepts, solve 22−4+4=02x 2 −4x+4=0 using the quadratic formula =−±2−42x= 2a−b± b 2 −4ac​ ​ :Here, =2a=2, =−4b=−4, and =4c=4.Compute the discriminant:Δ=2−4=(−4)2−4⋅2⋅4=16−32=−16Δ=b 2 −4ac=(−4) 2 −4⋅2⋅4=16−32=−16The discriminant is negative, so there are no real x-intercepts. The parabola does not cross the x-axis.Summary:The vertex of the function is (1,2)(1,2).The axis of symmetry is =1x=1.The y-intercept is (0,4)(0,4).There are no real x-intercepts.The parabola opens upwards (since >0a>0), has its vertex at (1,2)(1,2), and does not intersect the x-axis.

Answered by lusharis2 | 2024-09-05