question: consider the quadratic function $y = x^{2}-4x + 3$ for $0leq xleq5$. graph the function: plot the…

question: consider the quadratic function $y = x^{2}-4x + 3$ for $0leq xleq5$. graph the function: plot the function $y = x^{2}-4x + 3$ on a coordinate plane. label the x - axis as \x - value\ and the y - axis as \y - value\. mark the coordinates of all key points where the graph intersects the x - axis, reaches its minimum (since the coefficient of $x^{2}$ is positive, the parabola opens upward), and at least two other points that help show the shape of the parabola within the given interval.

question: consider the quadratic function $y = x^{2}-4x + 3$ for $0leq xleq5$. graph the function: plot the function $y = x^{2}-4x + 3$ on a coordinate plane. label the x - axis as \x - value\ and the y - axis as \y - value\. mark the coordinates of all key points where the graph intersects the x - axis, reaches its minimum (since the coefficient of $x^{2}$ is positive, the parabola opens upward), and at least two other points that help show the shape of the parabola within the given interval.

Answer

Explanation:

Step1: Find x - intercepts

Set $y = 0$, so $x^{2}-4x + 3=0$. Factor the quadratic equation: $(x - 1)(x - 3)=0$. Then $x=1$ or $x = 3$. The x - intercepts are $(1,0)$ and $(3,0)$.

Step2: Find the vertex

The x - coordinate of the vertex of a quadratic function $y=ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. For $y=x^{2}-4x + 3$, where $a = 1$, $b=-4$, $c = 3$, $x=-\frac{-4}{2\times1}=2$. Substitute $x = 2$ into the function: $y=(2)^{2}-4\times2 + 3=4-8 + 3=-1$. The vertex is $(2,-1)$.

Step3: Find other points

When $x=0$, $y=(0)^{2}-4\times0+3 = 3$, so the point is $(0,3)$. When $x = 5$, $y=(5)^{2}-4\times5+3=25 - 20+3=8$, so the point is $(5,8)$.

To graph: Plot the points $(0,3)$, $(1,0)$, $(2,-1)$, $(3,0)$, $(5,8)$ on the coordinate - plane. Label the x - axis as "x - value" and the y - axis as "y - value". Draw a smooth curve (a parabola opening upward) passing through these points.

Answer:

Graph with points $(0,3)$, $(1,0)$, $(2,-1)$, $(3,0)$, $(5,8)$ plotted and a smooth parabola drawn through them with x - axis labeled "x - value" and y - axis labeled "y - value".