2.4.1 Plot, interpret graphs of linear quadratic function

• How can you use the slope-intercept form to graph a linear equation?

  • Use the slope (m) to determine the direction and steepness of the line
  • Use the y-intercept (b) to plot the starting point of the line on the y-axis
  • Then plot additional points using the slope to determine the line's path
• The slope $m$ in the slope-intercept form represents the ratio of rise over run.


  True
• What does $m$ represent in the equation y = mx + c</latex>?


  Slope
• Steps to graph a linear function using the slope-intercept method:

  1️⃣ Plot the y-intercept

  2️⃣ Use the slope to find additional points

  3️⃣ Draw a straight line through the points
• What is the y-intercept formula?

  $b =$$y - mx$
• What is the slope formula?

  $m =$$\frac{y_2 - y_1}{x_2 - x_1}$
• How would you find the equation of a line given two points on the line?

  1. Use the slope formula to find the slope (m)
  2. Plug the slope and one of the given points into the slope-intercept form y = mx + b to solve for the y-intercept (b)
• The slope of a line indicates how steep it is.

  True
• What does the y-intercept (b) represent in the slope-intercept form?

  The y-intercept (b) represents the point where the line crosses the y-axis.
• In the equation $y =$$- \frac{3}{4}x +$$2$, what is the rise and run needed to plot the next point?


  Rise -3, run 4
• What is the x-intercept of the graph?

  The x-intercept is 1.
• What does the variable b</latex> influence in a quadratic function?

  Vertex position
• The equation $y =$$- \frac{3}{4}x +$$2$ represents a line with a negative slope.


  True
• What is the shape of the curve created by quadratic functions called?

  Parabola
• What is the y-intercept in the equation y = 2x + 3</latex>?


  3
• The general form of a quadratic function is y = ax² + bx + c</latex>


  True
• What is the vertex of the graph?

  The vertex is at the point (1, 2).
• What does it mean if a line has a slope of 3 and a y-intercept of 5?

  Crosses y-axis at 5
• What is the equation for the quadratic function in part b)?

  $y =$$-3x^2 +$$6x +$$1$
• What is the value of $a$ in the equation $y =$$2x^{2} - 5x +$$3$?


  2
• What is the equation for the quadratic function in part a)?

  $y =$$x^2 - 4x - 5$
• What is the y-intercept of the graph?

  The y-intercept is -3.
• The axis of symmetry divides the parabola into two identical halves.


  True
• The variable $c$ determines the y-intercept of the parabola


  True
• What is the axis of symmetry of the graph?

  The axis of symmetry is the y-axis.
• What is the equation for the quadratic function in part d)?

  $y =$$-2x^2 +$$8x - 11$
• How do you find the y-intercept of a quadratic function?

  Set $x =$$0$
• What does the slope (m) represent in the slope-intercept form?

  The slope (m) represents the rate of change or steepness of the line.
• The coefficient $c$ shifts the vertex of the parabola vertically.


  False
• What is the value of $b$ in the equation $y =$$2x^{2} - 5x +$$3$?


  -5
• What is the equation for the quadratic function in part c)?

  $y =$$4x^2 +$$12x +$$9$
• Match the feature with its corresponding value for the example graph:

  Vertex ↔️ (1, -4)

  X-intercepts ↔️ -1 and 3

  Y-intercept ↔️ (0, -3)
• What is the equation of the path of the ball?

  The equation of the path of the ball is:

  $h(x) =$$-16x^2 +$$64x +$$5$
• Steps to plot the graph of $y =$$x^{2} - 2x - 3$


  1️⃣ Plot the vertex (1, -4)

  2️⃣ Plot the x-intercepts -1 and 3

  3️⃣ Plot the y-intercept (0, -3)

  4️⃣ Draw a smooth U-shape using symmetry
• What is the value of $c$ in the equation $y =$$2x^{2} - 5x +$$3$?


  3
• What are the coordinates of the vertex?

  (1, 2)
• What is the value of the x-intercept?

  1
• How can you identify the key features of a quadratic function from its equation?

  • The coefficient of x^2 determines the direction of the parabola (positive = opens up, negative = opens down)
  • The constant term shifts the parabola up or down
  • The linear term (x) shifts the parabola left or right
  • The vertex can be found using the formula: x = -b/2a, y = f(x)
• Why does the path of the ball follow a parabolic trajectory?

  Due to the constant acceleration of gravity
• The line $y =$$2x +$$3$ has a slope of 2 and crosses the y-axis at 3.


  True