Multiple Choice
State the vertex, intercepts, and domain & range for each quadratic.
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12. Quadratic Equations and Functions
Graphing Quadratic Equations
Multiple Choice
Graph the following quadratics and state its vertex and intercepts.
A
Vertex: ; -intercept: ; -intercept:
B
Vertex: ; -intercept: ; -intercept:
C
Vertex: ; -intercept: ; -intercept:
D
Vertex: ; -intercept: ; -intercept:
Verified step by step guidance1
Identify the quadratic function given: \(y = -3x^2 + 10x - 3\).
Find the vertex using the vertex formula for a parabola \(y = ax^2 + bx + c\), where the x-coordinate of the vertex is \(x = -\frac{b}{2a}\). Substitute \(a = -3\) and \(b = 10\) to find \(x\).
Calculate the y-coordinate of the vertex by substituting the x-value found into the original quadratic equation.
Find the x-intercepts by setting \(y = 0\) and solving the quadratic equation \(-3x^2 + 10x - 3 = 0\) using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Find the y-intercept by evaluating the quadratic function at \(x = 0\), which gives \(y = c\).
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