Algebra 2 Practice - Graph the Quadratic Parabola y = -x^2 - 6x - 10 on a Coordinate Plane

Please subscribe!    / nickperich   To graph the quadratic parabola \( y = -x^2 - 6x - 10 \) on a coordinate plane, follow these steps: Step 1: Identify the Key Features The equation is in standard form \( y = ax^2 + bx + c \), where: \( a = -1 \) \( b = -6 \) \( c = -10 \) Step 2: Find the Vertex To find the vertex, use the formula for the \( x \)-coordinate of the vertex: \[ x_{\text{vertex}} = \frac{-b}{2a} \] Substitute \( a = -1 \) and \( b = -6 \) into the formula: \[ x_{\text{vertex}} = \frac{-(-6)}{2(-1)} = \frac{6}{-2} = -3 \] Now, substitute \( x = -3 \) into the original equation to find the \( y \)-coordinate of the vertex: \[ y = (-3)^2 - 6(-3) - 10 = 9 + 18 - 10 = 17 \] So, the vertex is \( (-3, 17) \). Step 3: Find the Axis of Symmetry The axis of symmetry is the vertical line that passes through the \( x \)-coordinate of the vertex. In this case, the axis of symmetry is: \[ x = -3 \] Step 4: Plot the Vertex and Axis of Symmetry Plot the vertex \( (-3, 17) \) on the coordinate plane, and draw the axis of symmetry, which is the vertical line \( x = -3 \). Step 5: Find Additional Points To get more points for the graph, choose values for \( x \) around the vertex (e.g., \( x = -2 \), \( x = -4 \), and \( x = -1 \)), and substitute them into the equation to find the corresponding \( y \)-values. For \( x = -2 \): \[ y = (-2)^2 - 6(-2) - 10 = 4 + 12 - 10 = 6 \] So, the point is \( (-2, 6) \). For \( x = -4 \): \[ y = (-4)^2 - 6(-4) - 10 = 16 + 24 - 10 = 30 \] So, the point is \( (-4, 30) \). For \( x = -1 \): \[ y = (-1)^2 - 6(-1) - 10 = 1 + 6 - 10 = -3 \] So, the point is \( (-1, -3) \). Step 6: Plot Additional Points Plot the points \( (-2, 6) \), \( (-4, 30) \), and \( (-1, -3) \). Step 7: Draw the Parabola Now that you have several points, draw a smooth curve through the points, forming an upside-down U-shaped parabola (since \( a = -1 \), which is negative). Final Graph Features: Vertex: \( (-3, 17) \) Axis of symmetry: \( x = -3 \) Parabola opens downward (since \( a = -1 \), which is negative) The parabola passes through the points \( (-2, 6) \), \( (-4, 30) \), \( (-1, -3) \), and others along the curve. The graph of the quadratic parabola should look like an upside-down U-shaped curve with the vertex at \( (-3, 17) \). I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: / nickperich Nick Perich Norristown Area High School Norristown Area School District Norristown, Pa #math #algebra #algebra2 #maths #math #shorts #funny #help #onlineclasses #onlinelearning #online #study